# Symbols Are an LSAT Taker's Best Friend

It's really important to know how to diagram sufficient and necessary statements (i.e. formal logic statements). This will be helpful for both the Logical Reasoning section and the Logic Games section.  There are two parts to a formal logic statement: the sufficient condition and the necessary condition."

Let's take for example the following sentence:"

If Melody keeps running, then her legs will get stronger.

Whatever part of the sentence you can place the "if" in front of is the sufficient part (i.e. "if" introduces the sufficient condition). So running is a sufficient way for Melody to strengthen her legs, but it is not necessary. Running is not the only way that Melody can make her legs stronger. Therefore "if Melody keeps running" is the sufficient part of the sentence. The other part of the sentence (i.e. the part that you can place the "then" in front of) is the necessary portion. If Melody keeps running, then it is necessary that her legs will get stronger. Though running is not the only way my legs will get stronger, if I run, they WILL get stronger."

"I always get nauseated after I've eaten a kiwi."

Which is the sufficient part? Me eating the kiwi or me getting nauseated? Think of it this way, am I telling you if I get nauseated, then I have eaten a kiwi, or if I eat a kiwi, then I get nauseated? They are similar sentences that are VERY different in LSAT land. The first version means that anytime I get nauseated the only culprit is a kiwi. The latter, which is a bit more realistic, means that I am allergic to kiwis but leaves open the possibility that other foods will also make me nauseated. I obviously meant the second one. So we have the sufficient being "after I've eaten a kiwi," and the necessary being "I always get nauseated.""

Now that we have down which part of the sentence is sufficient and which part is necessary, let's draw them out! Wait a minute, are you telling me I get to draw on the LSAT? Yes! Kinda… But, mostly yeah! So the sufficient goes on the left side and the necessary goes on the right side. Pick whatever letter or combination of letters that helps you remember what the phrase is and let's go! So I'm going to choose "N" for "I always get nauseated," and "K" for "after I've eaten a kiwi." Remember "K" is sufficient and "N" is necessary."

So we draw:"

K → N

We read the above "drawing" as follows: "If Melody eats a kiwi, then she gets nauseated." The "if" of the sentence is to the left of the arrow and the "then" of the sentence is to the right of the arrow."

Now, there is another crucial step to formal logic sentences. Every sufficient and necessary statement has a contrapositive. Please repeat. EVERY SUFFICIENT & NECESSARY STATEMENT HAS A CONTRAPOSITIVE. And you, my loyal LSAT minion, will NEVER forget to write out your contrapositive, ever! Okay so what is a contrapositive? It's easy to think of it this way, you will always know two certain things from every formal logic sentence you encounter on your LSAT. One will be the main logic statement, which is your "if/then" sentence you will form and draw out. The second is your contrapositive, which is a negated, flipped version of your first original sufficient and necessary statement."

So the contrapositive of our example is:"

N → K

We read the above "drawing" as follows: "If Melody is not nauseated, then she has not eaten a kiwi." You need to always remember that when you write out your contrapositive you need to REVERSE and NEGATE! I can't tell you how many students I've seen confused with their contrapositives because they have only done one of the steps! The contrapositive is really important because usually LSAC will try and trick you by writing the correct answer in contrapositive form. SO if you haven't written out your contrapositive, as you were supposed to, then you'll keep looking at your formal logic statement and wonder why it doesn't match with any of the answers provided. That's a recipe for a tantrum spewing LSAT student!"

Okay let's do one more example:"

"If Melody eats pizza, she will bloat. Melody is allergic to olives and will break out into hives if she eats them. If Melody does not eat dessert, she will be able to fit into her clothes."

I apologize for all my food based examples. I've got lunch on the brain! Okay so let's write it all out. I will have my contrapositives immediately underneath its respective sentence in red."

In order:"

If Melody eats pizza, she will bloat."

P → B

CONTRAPOSITIVE: If Melody is not bloated, then she has not eaten pizza."

BP

If Melody eats olives, she will break out into hives."

O → H

CONTRAPOSITIVE: If Melody has not broken out into hives, then she has not eaten olives."

H ? O

If Melody does not take eat dessert, she will be able to fit into her clothes.

D → F

CONTRAPOSITIVE: If Melody does not fit into her clothes, then she has eaten dessert."

F ? D

Well that's the basic idea of it all. Try and get the simple sentences down and always write their contrapositives. We will get into more complicated sentence constructions soon! Something that always helped me during my LSAT prep was to make everyday sentences into "if/then" sentences and practice, practice, practice!"

Happy Studying!"