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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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)
I am not sure what you mean by "can you use parity tables"Quote:
Originally Posted by andychallis
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
I suspect that is strictly up to the instructor.Quote:
Originally Posted by andychallis
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.
But my point is still this is a number theory study.Quote:
Originally Posted by andychallis
Have you proved each of those?
If you have, then you have proved the contrapositive.
Which means you have proved the theorem.