Dealing With Conditionals: Formalizing What you Already Know

There comes a time in every LSAT student’s life when they must learn stop worrying and love the conditional. Conditionals are just those little funny guys that we use to talk about, well, conditions. If….then, When….then… Unless …, then …. and so on.

Take a classic conditional:

1) If you have a cat, then fur will get all over.

We can make our lives a little easier by symbolizing the conditional like this:

1) If X, then Y.

Here, we just replace “you have a cat” with X, and “fur will get all over” with Y. We can do this for similar reasons as we can replace numbers with variables in math: what matters for logic is just the structure of what’s being said. This can make our lives much easier on the test, as we won’t have to continually rewrite what was relevant.

We can even make this shorter and more concise by using arrow “—>.” to represent the logic that if…then represents. So we can just say

1) X —> Y

This is useful because it is easier to manipulate and also it gives a regular form to the conditional.

Now, it’s not uncommon to see conditionals written like

2) I only go out if I want a sandwich.

But we can’t just rewrite this as:

3) If I want a sandwich, I can go out.

This is because only if is actually a different logic than just if…then. Whenever we see “only if,” we treat that part of the sentence as the second part of the arrow. So really, (2) is written like

2) If I go out, then I want a sandwich.

The big thing to remember then is that “if…” by itself represents what goes in the first part of a condition, and “only if” represents the second part.

Because order matters when we put things into a conditional, we’ve given special names to the first and second piece. The sentence before the arrow is the antecedent. The sentence after the arrow is the consequent.

So

4) If I want to pet a cat, I have to be quiet.

Can be symbolized like

P —> Q

where P stands for “I want to pet a cat” and Q stands for “I have to be quiet.”

I want to pet the cat is the antecedent, and I have to be quiet is the consequent.

So, P is the antecedent and Q is the consequent.

With that, we have the language and symbolization to work with LSAT questions that require conditionals, like inference questions or parallel structure questions.

Try a few more symbolizations!

5) Only when I have coffee can I face the world.

6) If a tree gets big enough, it will only fall if it is cut down.

7) I’m usually angry, if I’m hungry.

8) The house is happy only if mom is happy.

—Ryan Born, 2/5/2025