Need help with a proof
The theory is: if 3 divides a^2 then 3 divides a.
Now, they ask for the contra-positive (p-q = ~p-~q), which will be: if 3 does not divide a then 3 does not divide a^2
So now how do you prove the contra-positive:
I'm not sure whether to use proof by cases, direct proof, or any of the other methods of proof.

Question

Need help with a proof
The theory is: if 3 divides a^2 then 3 divides a.
Now, they ask for the contra-positive (p->q = ~p->~q), which will be: if 3 does not divide a then 3 does not divide a^2
So now how do you prove the contra-positive:
I'm not sure whether to use proof by cases, direct proof, or any of the other methods of proof.

anonymous · Answer

Well I don't see what's wrong with proving the original statement and by modus tollens show that the contrapositive is true...

anonymous · Answer

If I was to prove anything here I would use variables and show how they factor...