Thread: can you use parity tables as proof?

can you use parity tables as proof?

I want to use it to prove this:

if mn is even, then at least one of m or n is even.

(very basic but can I use it as proof?? I have only been doing number theory for 2 weeks now)

Originally Posted by andychallis

can you use parity tables as proof?
I want to use it to prove this:

if mn is even, then at least one of m or n is even.

I am not sure what you mean by "can you use parity tables"

But you can prove the contrapositive.
If both m and n are odd then mn is odd..

m|n|mn
E|E|E
E|D|E
D|E|E
D|D|D

so when mn is even then 'm or n' must be even

Originally Posted by andychallis

m|n|mn
E|E|E
E|D|E
D|E|E
D|D|D

so when mn is even then 'm or n' must be even

I suspect that is strictly up to the instructor.
I would not use on a number theory question. But that is my view.

How did you get the values in your parity table? That is, how do you know the line "D D D"?

because m and n can be EE ED DE or DD, E=even D=odd, there are no other cases.

Originally Posted by andychallis

because m and n can be EE ED DE or DD, E=even D=odd, there are no other cases.

But my point is still this is a number theory study.
Have you proved each of those?
If you have, then you have proved the contrapositive.
Which means you have proved the theorem.