Question

Look at the statement below.

If a number is divisible by 8, it is an even number.

Which of these is a logically equivalent statement?

If it is not an even number, it is not divisible by 8.

If it is not divisible by 8, it is not an even number.

If it is an even number, it is divisible by 8.

If it is not an even number, it is divisible by 8.

Answer 1

if it is not an even number it is not divisible by 8

Answer 2

Try using the fact that, given two cases such that:
\[
P\implies Q
\]Then:
\[
\neg Q\implies \neg P
\]Where the little funky square bracket means 'not'.

Answer 3

If it is not an even number, it is not divisible by 8.

Answer 4

thanks guys