Thread: ab is odd

If ab is odd, then a and b are both odd. I'm not quite sure how to go about proving this. I think I need to assume ab is odd or maybe do a proof by contradicition?

Originally Posted by kathrynmath

If ab is odd, then a and b are both odd. I'm not quite sure how to go about proving this. I think I need to assume ab is odd or maybe do a proof by contradicition?

Just consider all the cases:

a and b odd,
a even b odd,
a odd b even,
a even b even.

CB

Originally Posted by CaptainBlack

Just consider all the cases:

a and b odd,
a even b odd,
a odd b even,
a even b even.

CB

But would that be an acceptable proof? I'm trying to do a formal proof.

Originally Posted by kathrynmath

But would that be an acceptable proof? I'm trying to do a formal proof.

The Captain gave the most straight forward and perfectly acceptable approach to the problem. as an alternative, you may want to use the contrapositive, then you only have to check 3 cases

Assume a and b are not both odd, then you have 3 cases:

(1) a is even but b is odd
(2) a is odd but b is even
(3) a and b are both even

in all cases, we have ab even, so the proof by contrapositive follows