I am given this sort of problem:
Prove the following statement using a proof by contraposition.
$∀n∈Z$, if $n^2 \bmod 5=1$ then, $n \bmod 5=1$ or $n \bmod 5=4.$
So, the contrapositive would be:
$∀n∈Z$, if $n\bmod 5≠1$ or $n\bmod 5≠4$ then, $n^2\bmod 5≠1$
My problem here is how would you prove that such elements do not equal to each other?