Question

Which of the following is contrapositive of “If x is divisible by 4 then x must be divisible by 2”?

(a) If x is divisible by 2 then x must be divisible by 4

(b) If x is not divisible by 2 then x must be divisible by 4

(c) If x is not divisible by 2 then x is not divisible by 4

(d) If x is divisible by 4 then x is not divisible by 2

I have been asked this question in an online interview.

Enquiry is from Mathematical Reasoning topic in division Mathematical Reasoning of Mathematics – Class 11

Answer 1

Right choice is (c) If x is not divisible by 2 then x is not divisible by 4

Easy explanation: Contrapositive statement for given statement “if p then q” is “if not q then not p” i.e. ~q => ~p.

So, contrapositive for “If x is divisible by 4 then x must be divisible by 2” is “If x is not divisible by 2 then x is not divisible by 4”.