Consider the statement: ‘For all integers n, if n is a multiple of 6, then n is a multiple of 2’ - HSC - SSCE Mathematics Extension 2 - Question 4 - 2021 - Paper 1

To find the contrapositive of the given statement, we start with its structure: 'If P, then Q', where P is 'n is a multiple of 6' and Q is 'n is a multiple of 2'.

The contrapositive negates both parts and flips them, resulting in 'If not Q, then not P', which translates to 'If n is not a multiple of 2, then n is not a multiple of 6'. Thus, the correct answer is:

C. For all integers n, if n is not a multiple of 2, then n is not a multiple of 6.