Logical Conditions

Logically Valid Inference

Also referred to through entailment and inference.

Things that must be true if the premises are true.

• However, in LR and RC sections of the LSAT, the words "infer" and "imply" will sometimes refer to nondeductive inferences.

Conditional Statement

Expresses a relationship where the truth of one statement (the necessary condition, A) is dependent on the truth of another (the sufficient condition, B).

• These statements are often expressed as "if/then" sentences. Crucial for identifying valid inferences and recognizing potential flaws in arguments. 

Contrapositive

A contrapositive is formed by flipping and negating both parts of a conditional statement—and it’s always logically equivalent to the original, so if one is true, the other must be true too.

Standard Format:

• Original: If A, then B → A → B

• Contrapositive: If not B, then not A → ¬B → ¬A

• If the contrapositive is true, then the original conditional statement is also true.

• If you are a pilot (P), then you have good vision (V). P - V

  • “Not V” becomes the antecedent; “not P” becomes the consequent.

• If someone doesn’t have good vision, then they are not a pilot → ¬V → ¬P ✅

Logically Equivalent

When two statements have the same truth value. They are both either true or false in every possible situation. They may look different, but they mean the same thing logically.

Converse

Shows up as wrong answer choices in Logical Reasoning. They sound like they make sense, but they’re not valid conclusions. You can’t assume the truth of the converse or inverse just because the original is true.

• Look for an “If..., then...” structure.

• You’re trying to find the original A → B statement.

• Switch the order (If someone is a surgeon, they went to medical school A - B)

• (B - A If someone went to medical school, they are a surgeon).

• Flip statement A and B. But do not negate.

• If the statement is not valid flipped, it is not logical.

Inverse

In logic, when you're dealing with conditional ("if-then") statements, the inverse is what you get when you negate both parts of the original statement without flipping the order.

Formula: If the original is: A → B. Then the inverse is:¬A → ¬B

If it is a cat, then it is a mammal.
(Cat → Mammal)

Inverse:

If it is not a cat, then it is not a mammal.
(¬Cat → ¬Mammal) ❌ This is not valid.

If, then Statement