TMUA Logic Drill · Necessary Conditions

Very Easy · Paper 2 Style

Which statement is equivalent to:

“A number is divisible by 6 only if it is divisible by 3.”

A. If a number is divisible by 3, then it is divisible by 6. B. If a number is divisible by 6, then it is divisible by 3. C. A number is divisible by 6 if and only if it is divisible by 3. D. A number is divisible by 3 only if it is divisible by 6.

Correct answer: B

Solution: The phrase “P only if Q” means if P, then Q.

Here, $P$ is “the number is divisible by 6” and $Q$ is “the number is divisible by 3”.

So the equivalent statement is: If a number is divisible by 6, then it is divisible by 3.