Formal Logic is a set of rules for making deductions in an argument. When you use formal logic you transform arguments into mathematical-like diagrams. Below are 11 of the most common ways you will see formal logic appear in sentences on the LSAT:
- If A then B: A—> B
Example: If I go to the store then I will pick up milk
Go to store —> get milk
But, going to the store is just one way I can get milk. It is not the only way. I could get milk from a farm, etc. But, what I do know is that if I go to the store I will 100% get milk there.
- All C are D: C —-> D
Example: All flowers are pretty.
Flower —> pretty
Therefore, if you are a flower then you are also for sure pretty. However, there are pretty things that aren’t flowers, such as people, beaches, etc. So all you know for sure is that if it is a flower then it is 100% pretty. OR if it is ugly then it for sure isn’t a flower.
- Every E is F: E —-> F
Example: Every dog likes walks
Dog —> likes walks
Therefore, every dog in the world likes walks, but there can be other things or animals that also likes walks. You just won’t find a dog out there that doesn’t like walks, so if you find a creature that doesn’t like a walk it won’t be a dog.
- No G are H: G —> ~H
Example: No fish can fly.
Fish —> can’t fly
Therefore, if you are a fish then you 100% cannot fly. However, if you can’t fly that doesn’t mean you are a fish. You could be a person, and people can’t fly either. All we know for certain is if you can fly then you aren’t a fish.
- Only I are J: J —> I
Example: Only Zombies eat brains.
Eat brains —> Zombie
Therefore, if you eat brains then you must be a zombie. However, being a zombie doesn’t mean you have to eat brains. You could eat only hearts perhaps instead. On the other hand, if you find yourself eating a brain then you are 100% a zombie.
- K only if L: K —> L
Example: Kelly will go to the movies only if Laura goes too.
Kelly movies —> Laura movies
Therefore, if you see Kelly at the movies then Laura must be there as well. However, Laura can go to the movies without Kelly. But, if Laura does not go to the movies we 100% know Kelly is not going either.
Tip: Replace the “only if” with “then”. Statement will read if K then L. What follows the “if” goes on the left side of the arrow and what follows then goes on the right side of the arrow.
- The only M are N: M—-> N
Example: The only people who eat brains are zombies.
Person who eats brain —> Zombie
Therefore, once again if you find yourself eating brains then you must be a zombie. But, as a zombie you don’t have to eat brains you can snack on other things.
- No O unless P: ~P —> ~O (O –> P)
Example: No dessert unless you finish your dinner
Don’t finish dinner —> no dessert (dessert—> finished dinner)
Therefore, if you do not finish your dinner then you do not get dessert. However, if you finish your dinner that doesn’t mean you for sure are having dessert. Perhaps you are full and you don’t want dessert anymore. The only thing that statement tells us is if you are eating dessert then you must have finished your dinner.
Tip: Replace the “unless” with “if not” and then read the statement starting at the “if”. If not finish dinner then no dessert (~finish dinner —> ~ dessert). What follows the “if” goes on the left side of the arrow and what follows then goes on the right side of the arrow.
- No Q without R: Q —> R
Example: You won’t get a 180 on the LSAT without studying
Got a 180 on LSAT —> studied
Therefore, if you scored a 180 on your LSAT then you must have studied. It is impossible to get a 180 on the LSAT if you don’t study. However, studying doesn’t guarantee that you will get a 180 on the LSAT unfortunately.
- S if but only if T: S <—> T
Example: You will feel rested tomorrow if but only if you go to bed by 10 pm.
Feel rested tomorrow <—> bed by 10 pm
Therefore, if you feel rested tomorrow then you went to bed by 10 pm. And if you went to bed by 10 pm then you will 100% feel rested. These phrases: “if and only if” and “if but only if” means the relationship between the two variables goes both ways.
- U is always V: U —> V
Example: Ursula is always a villain in the little mermaid.
Ursula —> villain in little mermaid
Therefore, if you are the sea-witch Ursula then you are 100% pure villain. If the character isn’t a villain in the movie then that character cannot be Ursula.