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?

Results 1 to 4 of 4

- November 4th 2008, 06:34 AM #1

- Joined
- Apr 2008
- From
- Vermont
- Posts
- 318

- November 4th 2008, 06:37 AM #2

- Joined
- Nov 2005
- From
- someplace
- Posts
- 14,972
- Thanks
- 4

- November 4th 2008, 06:39 AM #3

- Joined
- Apr 2008
- From
- Vermont
- Posts
- 318

- November 4th 2008, 07:42 AM #4
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