How to Define Atomic Radius in Chemistry

How to Define Atomic Radius in ChemistryIn chemistry, how to define atomic radius is important for creating chemical bonds. Creating these bonds helps prevent the chemical from reacting, as well as to keep it stable and to create better products. Without a way to define the radius of atoms in a substance, it would be difficult to determine what would happen if a chemical was heated up.The atom has a radius that is different for every atom in the substance. For example, carbon atoms have a higher radius than silicon atoms and then each other. The diameter of the atoms is defined as the widest distance between adjacent atoms.The distance between each individual atom can be measured in terms of the formula by which it is measured. Atomic Diameter is the measurement that is used to define the molecular radius of a substance.The formula used to measure the diameter of an atom is called Avogadro's Number. This number was originally created to help figure out how to break a solid into piece s. The formula is a constant measurement of the diameter of an atom. With this formula, it is easy to determine how many atoms a material contains.By knowing the formula for how many atoms there are in a substance, it is easy to get the diameter of a substance that is different from one substance to another. For example, two different solids may be the same density and size, but they will vary in diameter, so there will be one difference in the formula. Knowing this measurement is very important in chemistry.It is very easy to look at different substances and find a different diameter for each of them. For example, oil will be different in diameter than water and therefore different in weight. Different solids can have different numbers of atoms in them, and these numbers make all the difference in the world when trying to create different compounds.Defining the density of a substance is very important in chemistry. Density is simply the volume of a substance that includes the numbe r of atoms per cubic centimeter. A substance that is too dense is not able to hold any molecules, while a substance that is too light is too hard to stir it into a state that allows for the formation of molecular bonds.Using a formula such as this is a way to determine what the bond strength of a compound will be. Bond strength is a measurement of how easily the molecules will bond together when mixed together. The more molecules a compound can bond with, the stronger the bond between the molecules. Defining the atomic radius in chemistry is very important for creating new chemical bonds.

Top Tips To Help Your Child Learn To Read

Top Tips To Help Your Child Learn To ReadTutoring reading comprehension strategies can be of great help to teachers, especially when their students are struggling with this crucial subject. All children learn by practice and understanding. If you know how to find and fix the source of your child's frustrations, then you are in a good position to help him or her become a successful reader. Read on to find out some of the best tutoring reading comprehension strategies you can use in your classroom.Understanding what your child is reading. You have to understand why the reading is being done, because if you don't, then you can't really help your student understand it. It is essential to understand that reading comprehension strategies do not only rely on vocabulary but also on the overall structure of the text, including spelling and sentence structure. Ask your child what she understands about a particular topic. If there is any particular problem, then seek advice from an expert and g et more assistance.Understanding how your child processes information. A lot of students get confused at times, as they don't grasp the idea of learning from one point of view and from another. Don't rush your student in putting up reading comprehension strategies. One way to do this is to get a list of questions that you can ask your student, so that she can write down the responses.How to offer your child extra support. Sometimes the most helpful tutoring strategies are freebies that your student is offered at home. In case you have all the material that your student needs, and if you have got all the right teaching tools, then you can go for the traditional reading comprehension strategies. This includes reading aloud to your child, reading aloud in front of your child, using photos and visual aids, and many other tricks. The best part is that these tutoring reading strategies are cost-effective, but they provide real benefits.You need to understand that nothing in this world is perfect. Trying to understand why your child does not understand a particular topic is important because it helps you understand the direction your child is headed. When you are giving your child feedback and instructions, don't forget to explain the reason behind it. This is one of the best teaching strategies that you can use.How to make your child understand what is meant by different types of supplementary reading comprehension strategies? These include special books, educational games, online reading help, and lots of other help. Giving your child additional help is a good way to make your child understand what you are trying to convey. The important thing is that the teacher always follows instructions and never makes a suggestion which will upset your child. If your child is struggling with his/her reading, ask your child what she is getting confused about.Tutoring reading comprehension strategies can be of great help for every teacher. Remember that the techniques offered in these strategies are not merely teach your child to read, but rather these strategies are designed to teach your child to learn. These help you understand the importance of reading and enrich your child's experience in this life.

Top 10 French Recipes

Top 10 French Recipes Top 10 Best French Dishes ChaptersDauphinoise PotatoesPot Au FeuCoq Au VinQuiche LorraineSteak TartareCassouletBeef BourguignonBouillabaisseMusselsBourgogne SnailsCooked by their grandmothers, these dishes are the epitome of France’s childhoods. These meals hold a special place in people’s hearts and hold memories that are hard to recreate as an adult.Of course, even though we have relied on various internet polls our Top 10 remains subjective. The list will inevitably miss thousands of variations and some regions may consider themselves underrepresented.With French gastronomy so incredibly rich the hardest thing was the limit the list to 10…it could have gone on forever!If your favourite dish is missing from our list, share it with your fellow Superprof readers in the comments below!Tartare, comes from, as the name suggests, Tatars (now Ukraine) before it reached the rest of Europe and was adopted by the French.Nowadays you’ll find beef tartare on the menu but traditionally the dish was made with hor se meat. This may sound horrible to us but it is actually very healthy, has a more distinct taste and is less prone to diseases than beef.From one chef to another the way of serving this dish varies; in small cubes, large cubes or served as a haché (like a raw patty).The real differences are found in the accompanying sides. Some serve it with a raw egg on top, with bread and salad, or some serve it with fries.Learn to make it in our cooking classes!CassouletThere has been some debate on the origins of this dish. But it seems to be the city of Castelnaudary in the south of France that has made the most convincing claim, and is now thought of as the Capital of cassoulet!The dish mixes dry beans (usually tarbais â€" a white bean) with pork rind, sausage from Toulouse or duck confit, plus lots of herbs and spices!It’s a great family meal, and accompanied with a quality red wine will warm you up on a winter’s day just before taking an afternoon nap!Beef BourguignonA staple on menus across France (Source: Pexels)Much like stew (the only difference is that the meat is marinated in alcohol before cooking and pig’s feet are often added) this dish is a firm favourite in France and in restaurants around the world.The Bourgogne region can boast about creating this speciality which transforms simple meat into a deliciously rich dish.You must, of course, choose an excellent Bourgogne wine, and don’t forget mushrooms, lard and onions.There is no set accompaniment so you have the freedom to decide what you serve with it: pasta, potatoes or vegetables!BouillabaisseNow we’re going right down to the south of France to get a taste of the Mediterranean.This dish is one of the staples of provincial French gastronomy, where seafood plays a central role.Bouillabaisse is a sort of fish soup made with whole cuts of fresh fish and potatoes and is garnished with garlic or crispy croutons.Cuts of inexpensive fish are used for this soup that we wouldn’t usually eat by themselv es.This dish is straight from fisherman’s families who concocted a recipe to use up the fish they couldn’t sell at the market, and now people can’t get enough of it!MusselsGoing back to the other end of France, to the north, we find a speciality that can also be found across the border in Belgium.‘Moules-Frites’ (mussels and fries) is a staple on menus along the coast of France and indeed across the country, but few people know that the ‘sauce marinière’ that accompanies mussels actually originates in Charentes in the south west of France.It could not be simpler but this dish is delicious, it’s made up of chopped parsley, white wine, shallots, pepper and some sort of fat â€" either olive oil or butter depending on who you ask!). Some fries on the side make it the perfect meal!Bourgogne SnailsTry the most French dish of all, snails!   (Source: divinefishandmeat.com)We return once more to Bourgogne to a dish that along with frog’s legs has become the stereotype of t he French diet for most of us non-French people!Snails are mostly eaten around Christmas time and typically the helix pomatia is the species of choice!First, they are taken out of their shell and then baked in either parsley or garlic butter (which makes them a lot more palatable!). Then they are put back into their shells to be served.Mop up the sauce with a crusty baguette and you have a delicious meal!Do you know much about the History of French cuisine?Or about the diversity of regional French cuisine?Finally, discover more about  French Gastronomy.

The Numerous Advantages of Online Tutoring

The Numerous Advantages of Online Tutoring 0SHARESShare Once you have enrolled yourself for an online tutoring program  you will discover the immense advantages of this mode of learning. The foremost advantage is that of convenience. You are sitting at home and being guided by a learned teacher who maybe sitting thousands of miles away. There is a tremendous amount of time saving when you go for online tutoring. You do not have to waste time in commuting to a distant classroom. You also save money that you would have had to spend on transportation. Online tutoring is also very efficient. You have a vast library of audio video files available to you once you enroll for an online tutoring program. You can study these in your spare time. You now also have the confidence of knowing that someone is there to help you with your homework. Earlier you could not turn to anyone for guidance. Now at the appointed time your online tutor will help you understand difficult subjects. This medium of learning is full of advantages. [starbox id=admin]

Covariance Equation

Covariance Equation Covariance equation is the important part of the statistics. This tool is helpful in finding out the covariance. But this involves important considerations. To understand this equation we need to first understand the meaning of mean, as mean is very important in finding out the covariance. In simple words, mean is defined as the sum of all terms divided by the number of terms. The following steps are the basics to calculate the covariance. This is all part of covariance equation. First step is to calculate the mean of first variable (X) and second variable (Y) Multiply each data entry point of first (X) with second variable (Y). Next step is to calculate the mean of obtained terms in step II (XY). After this step we need to find out the product of mean of X and Y. Last step is to find out the difference between the mean obtained in step 4 (X and Y) from the mean obtained in step 3 (XY). That is: - mean (XY) mean (X Y). This calculated difference is covariance. Example 1: Two variables are given X (1, 1, 1, 1) and Y (2, 2, 2, 2). Find the covariance. Solution: Given two variables, X (1, 1, 1, 1) and Y (2, 2, 2, 2) To find: - Covariance Step 1:- Mean of X = (1+ 1+ 1+ 1)/4 = 4/4 = 1 Mean of Y = (2+ 2+ 2+ 2)/4 = 8/4 = 2 Step 2:- Now we need each data point of X and Y that is (2x1, 2x1, 2x1, 2x1) = (2, 2, 2, 2) Step 3:- Now the mean of XY = (2+2+2+2)/4 = 8/4 = 2 Step 4:- Next step is to multiply the mean of X and Y, that is 2 x 1= 2 Step 5:- Therefore Covariance = 2 2 = 0. Since covariance is zero, therefore it is known as uncorrelated. Example 2: Two variables are given X (4, 4, 2, 2) and Y (2, 2, 2, 2). Find the covariance. Solution: Given two variables, X (4, 4, 2, 2) and Y (2, 2, 2, 2) To find: - Covariance Step 1:- Mean of X = (4+ 4+ 2+ 2)/4 = 12/4 = 3 Mean of Y = (2+ 2+ 2+ 2)/4 = 8/4 = 2 Step 2:- Now we need each data point of X and Y that is (2x4, 2x4, 2x2, 2x2) = (8, 8, 4, 4) Step 3:- Now the mean of XY = (8+8+4+4)/4 = 24/4 = 6 Step 4:- Next step is to multiply the mean of X and Y, that is 3 x 2= 6 Step 5:- Therefore Covariance = 6 6 =0 Since covariance is zero, therefore it is known as uncorrelated.

Top 10 Online Tutoring Schools

Top 10 Online Tutoring Schools With the internet penetrating and connecting every nook and corner of the world, the online platform has garnered a lot of popularity in various sectors such as commerce, finance, health and education. Particularly in education, this platform finds excellent use for students these days opt for online learning. With a lot of demand for round the clock help and expert support 24*7, many top notch universities and schools today offer online tutoring services. Here is a list of the top 10 online tutoring schools and the kind of services that they offer; read on. Binghamton University This popular State University of New York offers a variety of free online tutoring programs for students who have enrolled with the University. Qualified and proficient tutors are handpicked for these sessions and the lessons are offered in the following subjects: math, writing, accounting, biology and chemistry. These services are open for five days a week from Sunday through Thursday and taught from 7 pm till midnight. Students are sure to benefit from such classes as the subjects chosen for these classes are conducted are usually the problem makers for most students. St. Petersburg College This eminent college offers 24*7 online tutoring services for a variety of courses through its SmartThinking platform. There is an impressive ‘Drop in Tutoring’ feature that lets the students connect with a live tutor to work on their problem areas. This feature is available for a wide variety of subjects from arts and humanities to social and behavioral sciences. Yet another interesting feature is the Writing Center wherein a student can upload his/her paper or assignment and get it reviewed by subject experts. With such hands on help students are sure to get top notch grades in their exams and maintain a good GPA. UCLA Engineering UCLA Engineering offers free online tutoring to middle and high school students in the Southern California region. Students at UCLA Engineering are voluntary tutors in this program and it is designed to help students with tricky areas in math and sciences. Homework help, clarification of doubts, discussion forums and live interactions are the different learning options available to students in this amazing platform. Numerous schools are participating in this outreach program and have benefitted from it and students find it easier to communicate and learn in this platform as there are a number of innovative tools such interactive whiteboards that are employed to help students learn better. Fulton Schools of Engineering Fulton Schools of Engineering offers free online tutoring programs to students pursuing their under grad courses at the Arizona State University. The competition and difficulty at under grad levels are too high today and students find the need for additional help to cope with the stress and standards of today’s education. The online classes are open from 4-9 pm through the week and from 2- 9 pm on Sundays. Review sessions, workshops, options to interact with tutors without enrolling (as guests) and so on are available with these online tutoring sessions. The online classes are available for a variety of subjects and are conducted in a manner that is conducive to learning. Arizona State University The Arizona State University’s tutoring sessions are built around the concept â€" ‘Access Assistance Anywhere’. This succinctly captures the whole idea behind online tutoring and allows interactions with peer tutors (who have completed the classes on which the student seeking tutoring has currently enrolled. Innovative learning tools such as interactive whiteboards are employed in this forum and the tutors use power point slides and pdf documents to clarify doubts. Sessions are even recorded to allow for review later and the tutors are available from Sunday through Friday. On call assistance is available through the week and apart from this review sessions, online mentoring and online guides and videos too are available to help students learn better. New York Institute of Technology NYIT offers online tutoring services via Brainfuse and offers help in a variety of subjects such as math, physics, college writing, life sciences, business, accounting, resume help and computer literacy. Help for some of the subject areas are available throughout the day and round the clock with live tutors! With expert help being available 24*7 on a wide variety of subjects, students find it easier to cope with complex topics. Also, students have to be prepared with their questions in advanced to seek the tutor’s help and this ensures that they actually put in the requisite effort before connecting with a tutor. College of Staten Island Apart from drop in tutoring options, the College of Staten Island also offers online tutoring services. The online classes are free and students can avail them in the following subjects: English writing, History Core 100, Math, Physics and Spanish. These tutoring sessions serve to supplement class-room learning and any subject area that the student finds difficult can be addressed in these sessions. Tutors also offer help with essays, take-home exams and help students hone their presentation and writing skills so that they can turn in better assignments and essays. Math Tutor Math tutor is a website that offers innovative learning solutions to facilitate easier learning of middle school math. This is a free website and students get to enjoy the use of intelligent software tutors. Students receive step by step explanations and feedback and these software solutions were built at the Carnegie Mellon University after extensive research and thus provide for a rich and comfortable learning experience for students. The curriculum and content available is aligned towards NCTM Focal Points and Common Care Domains. Students find it rewarding and fun to learn with such intelligent software and this technology has a proven success record. MiraCosta College MiraCosta College provides live and mail based tutoring services as part of the Western eTutoring Consortium of Colleges Universities. Easy and fun to learn, this platform offers tutoring in many subject areas where students struggle to get good grades and they are: accounting, calculus, chemistry, physics, anatomy physiology, biology, economics, engineering, psychology, Spanish, web development, statistics, Microsoft office and math. A variety of options such as eChat, eQuestions, eWriting lab, student tutorials and resources are available to help students with their problem areas. Lorain County Community College eTutoring services are offered at Lorain County Community College and the college is a member of eTutoring.org. Classes are provided in a wide range of subjects from biology, chemistry, writing, math, accounting and calculus II. With multiple options for tutoring such as eQuestions, eWriting, eChat and resources, The LCC Tutoring Center does offer the students a lot of flexible options to choose from and this in turn helps them understand better as they can choose the right medium for themselves to learn and improve their GPAs. Tutor Pace is a leading online tutoring services provider with a wide array of professional tutoring services in a variety of subject areas. With a lot of interactive and innovative learning tools, eminent tutors and flexible learning options, Tutor Pace offers an excellent online learning platform for students at pocket-friendly rates. The assignment help services and homework help provided are top notch and students find it easier to voice their doubts and thus learn better and score high under the tutelage of the professional online tutors employed here.

Should I Go To Harvard University

Should I Go To Harvard University The tutors behind Varsity Tutors are not just here to teach theyre sharing their college experiences as well. Michele is a Chicago tutor specializing in LSAT prep tutoring, Essay Editing tutoring, AP English tutoring, and more. She is a graduate of Harvard University with a Bachelors degree in English. Check out her review of her alma mater: VT: Describe the campus setting and transportation options.How urban or safe is the campus?Are there buses or do you need a car/bike? Michele: Harvard is nestled in the middle of the town of Cambridge, Massachusetts, right off of one of the public transit train stops (the T train). It is very easy to get around by public transit, and most students do not have or need cars (in fact, those who had cars often found them to be more trouble than they were worth given the cost of parking!). VT:How available are the professors, academic advisers, and teaching assistants? Michele: Professors, academic advisors, and teaching assistants are happy to make themselves available, but in order to make sure you have the best experience, be sure to take the initiative to seek them out. Make a note of professors and teaching assistants office hours and go to them. Be ready with a specific question related to the classs topic and be prepared to engage in a lively academic debate. Almost always, they will be glad you took the time to show up! VT: How would you describe the dorm life rooms, dining options, location, socialization opportunities with other students? Michele: Harvard has a system of houses, rather than dormitories, which goes back hundreds of years (literally!). Almost every house has its own dining hall, library, and common room. Although this is less true than in the past, each house has its own personality. Adams House, for example, was known to be academic and a bit quirky. A lot of the socialization on campus is based around the house you live in after your freshman year, so take advantage of dances / social hours at your house early on. You wont regret it, and your house may come to feel like a home. VT: Which majors/programs are best represented and supported?What did you study and why? Did the university do a good job supporting your particular area of study? Michele: Harvard has an excellent academic reputation, so it is difficult to identify particular programs or majors that stand out from others. Every major, from the fine arts to liberal arts to sciences, to engineering and mathematics has a stellar reputation, so its hard to go wrong. I studied English, in part because I was particularly impressed with the schools wide and deep offerings in Shakespearian studies. The university did an excellent job supporting my interest, and I was even able to help start a student organization that performed Shakespeares plays each semester. VT: How easy or difficult was it for you to meet people and make friends as a freshman? Does Greek life play a significant role in the campus social life? Michele: Harvard is a large university, even though its undergraduate campus can feel small. Many of my friendships from my freshman year began with my roommates and the people I met in different extracurricular activities. Greek life does not play a significant role in campus life. Especially early on, make the effort to talk to and get to know other students. This wont happen quite as easily as it would at a smaller school, but if you put in the effort, youll be well-rewarded (and you are likely to find that other students are eager to get to know their classmates as well). VT: How helpful is the Career Centerand other student support services?Do many reputable companies recruit on campus? Michele: Harvards Career Center is excellent, and in particular, the resume preparation advice I received there was invaluable (almost 15 years later, I still have and refer people to Harvards resume guide!). When it comes to recruiting, Harvards reputation will bring many companies to your doorstep. Almost any large company recruiting undergraduates will seek out and interview Harvard students. It will be up to you to close the deal, though! VT: How are the various study areas such aslibraries, the student union, and dorm lounges? Are they over-crowded, easily available, spacious? Michele: Harvards libraries are, in a word, gorgeous. And they are also excellent places to go to study. The Loker Reading room in Widener library is a beautiful and quiet place to focus and prepare for finals, for example. Because Harvard has houses rather than dorms, the house libraries are often where students study. Again, these are beautiful spaces and do not tend to be overcrowded. Dont expect them to be boisterous students are serious about study time! VT: Describe the surrounding town. What kinds of outside establishments / things to do are there that make it fun, boring, or somewhere in between?To what extent do students go to the downtown area of the city versus staying near campus? Michele: One common joke among Harvard students was that a student was more likely to visit New York City than downtown Boston. Its surprisingly easy to get to New York City from Cambridge, and many students make the trip on the weekends. The city of Cambridge is a nice college town with a mix of coffee shops, book stores, and small restaurants. There isnt a large bar scene but there are a variety of small pubs. The movie, Good Will Hunting, wasnt far off here! VT: How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Michele: Harvards undergraduate student body is approximately 4,000 students larger than many students think. Class sizes vary widely and shrink significantly (from over 100 students to 6-10 students) once you begin taking upper-level classes. One little-known fact is that some graduate courses can be open to undergraduate students upon permission of the professor. If you develop a good relationship with a professor early on, consider asking that professor if you might be able to take his or her graduate-level course. VT: Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one youregretthe most. Michele: One of my favorite Harvard memories is a lecture a professor gave on the life and work of the author, Virginia Woolf. She cared so passionately about the subject and constructed the lecture so well that it went far beyond being informative it was powerful and moving. Thats the only time I have ever seen a spontaneous standing ovation for a lecture! Check out Micheles tutoring profile. The views expressed in this article do not necessarily represent the views of Varsity Tutors.

3 Ways to Enhance Your Graduate School Application

3 Ways to Enhance Your Graduate School Application When you apply to graduate school, think of your application as your first encounter with someone whom you admire. You want to make a positive first impression. While the application may seem two-dimensional, its different parts provide ample opportunities through which you can highlight your strengths. You may find thiscollege student's guide to applying to grad schooluseful as well.As you compile your essays, recommendations, transcripts, and resume, check out these three ways to creatively enhance your graduate school application. 1. Draw on your unique background and experiences When you write your essays and resume, reflect on what makes you unique. Think about the clubs in which you have participated and the leadership roles you have taken on, especially those that relate to your intended field of study. By showing you exceeded what was required of you, especially in an academic setting, you are sure to stand out. In addition, consider mentioning any jobs and internships you have held in the past. Do not discount part-time or volunteer experiences; they can also help demonstrate to admissions officers your seriousness about pursuing graduate school. These are some great tips on how to write a resume for grad school applications. Assess your experiences outside of school and work as well. To where have you traveled, either in your free time or through a program? What about your personal background? Did you move around much as a child, which forced you to adapt quickly to new situations? Or did you stay in one place and get to know your community well? Are you passionate about a certain cause? How would you diversify your prospective schools student body? Pinpointing your unique characteristics will help your graduate school application to stand out. 2. Research and connect with the school Get familiar with the schools to which you are applying. Adjust your applications for each school. Browse the university website, and take note of what the university values in prospective and current students. Do they emphasize certain values over others, such as leadership, teamwork, or diversity? Next, think about how your own interests and experiences relate to those values. If you relate your priorities to those of the institution, admissions officers will be impressed. If you can, schedule formal or informal interviews. Begin casual correspondence with the admissions department, the department of your intended major, or alumni. This interaction will aid you in getting to know the school better. The simple act of reaching out could even add points to your application you never know! 3. Include a relevant anecdote The main goal of the application essay is to show that you are a thoughtful, articulate individual. Admissions board members will notice how hard you have worked through your transcripts and resume; it is the essay where your voice and personality shine. At the beginning of your essay, include a personal experience that strongly relates to your intended field of study. Consider turning points in your life for example, when you were first inspired to pursue your line of study or when you gained greater traction in the field. Did you have an experience during your childhood, adolescence, or young adult years when you were challenged and learned something monumental? Seek out ways to relate these experiences to your goals and your desire to study at that specific school. There is nothing more humanizing and balancing to the application than a relevant and well thought-out personal story. This is a great list of the best classes for grad school admissions. You will spend much time self-reflecting throughout the graduate school application process. Remember that you have a lifetime of experiences you can include; relate them to the university you wish to enter. The admissions department will be able to read the confidence in your application, both in your past studies and prospective studies at their institution.

How to Use Conditional Reasoning to Crush LSAT Logic Games

How to Use Conditional Reasoning to Crush LSAT Logic Games LSAT Law School Blog The LSAT Logic Games section is the shortest section of the LSAT. Yet it often provokes the strongest feelings among LSAT test-takers. People either love this section, or they hate it. Both sides have a point. LSAT Logic Games either confuse or stimulate curiosity. The key to doing well on, and mastering, these Games is paying careful attention to detail. Pay very careful attention to the information these Games present, and extract as much additional data from that information as possible. One area where this skill can be applied is in conditional reasoning. The LSAT Logic Games section often uses conditional reasoning (e.g., If A, then B) to express one or more rules, ask questions, and, in the process, confuse students. The key to overcoming the LSAT’s use of conditional reasoning is to understand critical differences between conditional statements and then to use these statements to draw helpful inferences. What is Conditional Reasoning? Conditional reasoning is an area of logic that is prevalent mostly on the Logical Reasoning and Logic Games sections of the LSAT. It involves the use of “sufficient” and “necessary” conditions. Students should have a firm grasp of these concepts in general to perform well on the LSAT. A “sufficient” condition literally refers to something that is “enough.” It implies the existence of something else. On the LSAT, it will usually take the form of the statement “If A is in Group 1, then B is in Group 1.” That means that the condition “A is in Group 1” is sufficient for B to be in Group 1. In contrast, a “necessary” condition literally refers to something that is “required.” Unlike a sufficient condition, it does not yield an inference. Thus, the condition above that “B is in Group 1” does not mean that A is also in Group 1. It simply means that it is possible A could be in Group 1. How the LSAT Uses Conditional Reasoning to Confuse Students The LSAT will attempt to make students confuse something that is required for an event to occur for something that is sufficient for an event to occur, and vice versa. Let’s consider the following hypothetical example on an LSAT Logic Game: If Braden is placed in English 102, then Celeste is not placed in English 102. This is a common rule that appears on a Logic Game that involves pure grouping where certain variables are either “in or out” of a certain arrangement. This particular Game will usually entail some grouping of students in a class, and the rules that are provided will require you to plug in certain students in that class and exclude others. The rule above tells us that, if Braden is placed in English 102, that event implies that Celeste will not be placed in English 102. We would diagram this rule as follows: B -- C The contrapositive of this rule would be, “If Celeste is placed in English 102, then Braden is not placed in English 102.” We would diagram the contrapositive as follows: C -- B Now consider if one of the rules or questions in this Logic Game presented you with the following slightly different statement: If Braden is not placed in English 102, then Celeste must be placed in English 102. This is a slightly different statement, but it has major implications when it is applied. In contrast to the first rule above, this second rule tells us that, if Braden is not placed in English 102, then that event implies that Celeste will have to be placed in English 102. We would diagram this rule as follows: B -- C The contrapositive of this rule would be, “If Celeste is not placed in English 102, then Braden must be placed in English 102.” We would diagram it as follows: C -- B These two rules appear similar, but they apply themselves differently. The test writers will often try to confuse you with similarities like these. You will have to recognize the differences and diagram/document them correctly. How to Use Conditional Statements to Identify Scenarios Recognizing the differences between conditional statements is one thing. Using them to draw proper inferences is another animal altogether. This is where you earn your money on the LSAT. To perform well (or exceptionally well) on LSAT Logic Games, you need to infer additional rules from the rules that are provided. Developing and applying this skill will help you answer questions more quickly. If you are aiming for a very high score, it will, in part, mean the difference between missing a few questions on this section, and answering every question correctly. To draw proper inferences, it helps first to identify scenarios yielded by a given rule. Let’s do this with our first rule above: If Braden is placed in English 102, then Celeste is not placed in English 102. You will recall that we diagrammed this rule as follows: B -- C This rule yields FOUR potential scenarios. Your ability to recognize and document these four scenarios will determine how well you will perform on this particular Logic Game, and how quickly you can answer the questions. The four scenarios are the following: 1) B is placed in English 102; C is out This scenario is a straight application of the rule above. If B is placed in English 102, then C cannot be placed in the same class. Otherwise, it would be a violation of the rule. 2) C is placed in English 102; B is out This scenario is a straight application of the contrapositive of the rule above. If C (instead of B) is placed in English 102, then B cannot be placed in the same class. Otherwise, it would be a violation of the rule. 3) Both B and C are placed in English 102 = Not Possible This scenario is not possible and can never happen. Neither the rule (Scenario 1 above) nor its contrapositive (Scenario 2 above) permit this scenario from occurring. 4) Neither B nor C is placed in English 102 = Possible Although both B and C cannot be placed in English 102 (Scenario 3 above), it is possible for neither C nor C to be placed in English 102. The rule and its contrapositive do not prohibit this scenario. The rule applies only if either B or C is placed in English 102. If neither is placed in English 102, then the rule does not apply. If B was not placed in English 102, that does not mean C must automatically be placed in the class. Instead, C also could be excluded from English 102. Notice that these scenarios would not play out in the same way if, instead, we were dealing with a Logic Game that involved two separate groups (i.e., Team 1 or Team 2; or Group 1 or Group 2), where certain variables were either in one group or the other, as opposed to our Game above, where they are either “in or out.” In that case, the scenario where neither B nor C is selected would not be possible. However, here, it is possible because there is no other class (that we know of) where B or C could be placed. Our rule deals only with the people who are placed in English 102; it does not deal with the people who are not placed in English 102. Let’s now identify the scenarios yielded by our second rule: If Braden is not placed in English 102, then Celeste must be placed in English 102. You will recall that we diagrammed this rule as follows: B -- C Like our first rule, this rule yields FOUR potential scenarios: 1) B is not placed in English 102; C is placed in English 102 This scenario is a straight application of the rule above. If B is not placed in English 102, then C must be placed in the class. Otherwise, it would be a violation of the rule. 2) C is not placed in English 102; B is placed in English 102 This scenario is a straight application of the contrapositive of the rule above. If C (instead of B) is not placed in English 102, then B must be placed in the class. Otherwise, it would be a violation of the rule. 3) Neither B nor C is placed in English 102 = Not Possible This scenario is the opposite of our other Scenario 3. Whereas the former stated that placing both B and C in English 102 was not possible, this rule dictates that placing neither in English 102 is not possible. In other words, you can never have an English 102 class where both B and C are not placed in it. 4) Both B and C are placed in English 102 = Possible Although both B and C cannot be excluded from English 102 (Scenario 3 above), it is possible for both C and C to be placed in English 102. The rule and its contrapositive do not prohibit this scenario. The rule applies only if either B or C is not placed in English 102. If both are placed in English 102, then the rule does not apply. If B was placed in English 102, that does not mean C must automatically be excluded from the class. Instead, C also could be placed in English 102. Some students will get confused with this scenario and will not anticipate it. They will conclude that either B or C must be placed in English 102, but they will not conclude that both could be placed in the class. How to Use Conditional Statements to Draw Inferences As noted above, to perform well on LSAT Logic Games, you must draw as many inferences as possible from the rules provided. With respect to our first rule above (If Braden is placed in English 102, then Celeste is not placed in English 102; or B -- C), the first set of scenarios we predicted above help us draw two inferences: First, we can draw the inference that, at all times, at least either B or C will not be placed in English 102. This is reflected in Scenarios 1 and 2. When you diagram this Logic Game, you would make a note of this inference on your diagram. Second, we can draw the inference that there will never be a situation where both B and C are placed in English 102 (Scenario 3). Again, you would make a note of this inference on your diagram. Note that we cannot draw the inference that, at all times, at least either B or C will be placed in English 102. Rather, both could be excluded, as reflected by Scenario 4 above. With respect to our second rule above (If Braden is not placed in English 102, then Celeste must be placed in English 102; or B -- C), the second set of scenarios we predicted above also help us draw two inferences: First, we can draw the inference that, at all times, at least either B or C will be placed in English 102. This is reflected in Scenarios 1 and 2. You would make a note of this inference on your diagram. Second, we can draw the inference that there will never be a situation where neither B nor C is placed in English 102 (Scenario 3). You would note that as well on your diagram. Note that we cannot draw the inference that, at all times, at least either B or C will not be placed in English 102. Rather, both could be included, as reflected by Scenario 4. These are quick inferences you can make with this type of Logic Game. They don’t help you know everything about the Game, but they help you learn enough to help you answer certain questions rapidly. Conditional reasoning can often pose difficult problems for students. The key to overcoming these difficulties is to understand critical differences between conditional statements and then to use these statements to draw specific inferences that help you map out the possibilities in a Logic Game and then answer questions about those possibilities. About the Author: This article was written by Robert M. Fojo from LSAT Freedom. Robert graduated from Harvard Law School and is a co-founder of LSAT Freedom, an online LSAT prep course that emphasizes learning the logic on the exam and then applying that knowledge through practice with real LSAT questions. Robert frequently writes about tips and strategies for doing well on the LSAT. To get other helpful ideas for performing well on the LSAT and improving your score, join LSAT Freedom’s free newsletter hbspt.cta._relativeUrls=true;hbspt.cta.load(215486, '6baac2ae-05a3-4610-9d1f-265c8cbd809f', {});