Conditional Logic Doppelgangers
Diagramming Conditional Logic is a huge part of LSAT success, and can also be a major hurdle for many students to overcome. I’ve noticed over the years that there are two major sticking points in Conditional Logic for many of my students: pairs of conditional statements that look similar but mean different things. These Conditional Logic doppelgangers are if versus only if and mutually exclusive pairs. Let’s tackle both.
Conditional Logic Doppelganger #1: If Versus Only If
One of the most challenging Conditional Logic scenarios students face on the LSAT is the distinction between if and only if. These look very similar, but they diagram in completely opposite ways! Here’s an example:
Laura will buy a puzzle if it has more than fifty pieces.
More than fifty pieces → Buy Puzzle
Laura will buy a puzzle only if it has more than fifty pieces.
Buy Puzzle → More than fifty pieces
What’s the difference? Think of “if” as the impulse buyer and “only if” as the cautious buyer. “If” acts as a trigger—whatever follows it will always trigger the outcome, no matter what. This makes Laura into an impulsive puzzle buyer: anytime she sees a puzzle with more than fifty pieces, she’ll buy it. “Only if,” on the other hand, sets up a requirement, which makes Laura a cautious buyer. Having more than fifty pieces is no longer Laura’s only criteria for buying a puzzle; it’s just the first requirement. There could be many others! So all we know is that if Laura buys a puzzle, it definitely had more than fifty pieces.
The LSAT likes to use this distinction not only in Logic Games, but also in Logical Reasoning. A common LR flaw is to set up an argument that uses an “if” statement and then concludes that the “only if” version of the same statement is true; or vice versa. This is an invalid logical reversal. On harder questions, the LSAT will use the language sufficient and necessary to describe this flaw, because it confuses a sufficient condition (the left side of the conditional logic arrow, or the trigger) with a necessary condition (the right side of the arrow, or the guarantee). I usually encourage students to lump reversals, if/only if, and sufficient/necessary language into one mental bucket: if you see one of those things, be primed to spot the others as an answer choice or in the argument!
Conditional Logic Doppelganger #2: Mutually Exclusive Pairs
Mutually exclusive pairs create another common Conditional Logic trap. I think of it as the enemies versus study buddies distinction. Imagine you have the following rule:
If Spencer goes to the party, then Jake will not go to the party.
S → ~J
The contrapositive would be:
If Jake goes to the party, then Spencer will not go to the party.
J → ~S
In this case, Spencer and Jake are enemies. Each of them will refuse to go to the party if he hears the other person will be there. In this case, there’s no situation where both of them will be at the party. If this were a Conditional Logic game, we would say that one of the two will always be out. We could make a placeholder chart that looks like this:
It’s easy to make the mistake of thinking that this logic means either Spencer or Jake will definitely be at the party. But that’s not the case. Jake and Spencer could both not go to the party, and they’ll still be able to avoid each other (if they want to). Enemies can’t be in the same group together, but that doesn’t mean either of them has to be in the group at all.
The enemies example is more intuitive to most people than its counterpart, the study buddy example:
If Spencer does not go to class, Jake will go to class.
~S → J
The contrapositive would be:
If Jake does not go to class, Spencer will go to class.
~J → S
In this case, Jake and Spencer are study buddies. In order to make sure they’re both successful, they make a pact that if one of them is absent, the other one will definitely go to class. What’s the result? One of them will always be in class. On a Conditional Logic game, you could use this rule to make a placeholder chart like the one below:
A common misinterpretation of this rule is that it means Jake and Spencer cannot both attend class; one of them will always be out. But remember, their pact is designed to make sure that at least one of them is always in class. There’s nothing to prohibit both of them from going to class together; if they do, it just doesn’t trigger the pact (aka the Conditional Logic).
Got questions? Put them in the comments!
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Ally Bell is a Manhattan Prep instructor based in San Francisco, CA. Ally first encountered the LSAT while getting her Bachelor of Arts in English and history at Duke University. In college, she scored a 178 and very nearly applied to law school. In the end, she followed her true passion, teaching. As an LSAT teacher, she has the opportunity to blend her love for teaching with her passion for logical argument. Check out Ally’s upcoming LSAT courses here.