Logical Equivalence

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GRE Quantitative Reasoning › Logical Equivalence

Questions 1 - 1

Suppose A, B, and C are statements such that C is false if exactly one of A or B is true. If C is true, which of the following is also true?

Both A and B are both False

Both A and B are True

A is false, B is true

A is true, B is false

Step 1: Let's break down the logic problem...

C is false if A or B is True.

Example: C-False, A-True, B-False.

Step 2: Try to find what happens if C is true

If C is true, "or" changes to "and", and True becomes false..

So: C-True, A-False, B-False..

A and B must both be false for C to be true..

Answer: Both A and B are False.