# can you use parity tables as proof?

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• Oct 18th 2012, 11:26 AM
andychallis
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)
• Oct 18th 2012, 11:39 AM
Plato
Re: can you use parity tables as proof?
Quote:

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..
• Oct 18th 2012, 11:43 AM
andychallis
Re: 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 AM
Plato
Re: can you use parity tables as proof?
Quote:

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.
• Oct 18th 2012, 12:26 PM
HallsofIvy
Re: 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 PM
andychallis
Re: 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 PM
Plato
Re: can you use parity tables as proof?
Quote:

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.