TMUA Logic Drill · Necessary vs Sufficient

Hard · Paper 2 Style

Which statement is logically equivalent to:

x > 2 only if x² > 4?

A. x² > 4 ⇒ x > 2 B. x > 2 ⇒ x² > 4 C. x > 2 ⇔ x² > 4 D. x² > 4 only if x > 2

Correct answer: B

Solution: “P only if Q” means P ⇒ Q. Here P is “x > 2” and Q is “x² > 4”. So the equivalent statement is x > 2 ⇒ x² > 4.