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)

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- Oct 18th 2012, 11:26 AMandychalliscan 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) - Oct 18th 2012, 11:39 AMPlatoRe: can you use parity tables as proof?
- Oct 18th 2012, 11:43 AMandychallisRe: can you use parity tables as proof?
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 - Oct 18th 2012, 11:47 AMPlatoRe: can you use parity tables as proof?
- Oct 18th 2012, 12:26 PMHallsofIvyRe: can you use parity tables as proof?
How did you get the values in your parity table? That is, how do you know the line "D D D"?

- Oct 18th 2012, 12:44 PMandychallisRe: can you use parity tables as proof?
because m and n can be EE ED DE or DD, E=even D=odd, there are no other cases.

- Oct 18th 2012, 12:50 PMPlatoRe: can you use parity tables as proof?