# Indirect Proofs

1. Nov 30, 2005

### blimkie

use the method of indirect proof. if m and n are integars and there product mn is odd, prove that both m and n are odd

so i wnat to prove that (m)(n) odd (mn)

so i assume that (mn) is even to go about the indirect method

now i need a jump start i wrote some equations and some algebra but dindt come up with a contradication

help is appreciative thats alot guys

2. Nov 30, 2005

### Pyrrhus

Start off by

$$m = 2k+1$$

$$n = 2c + 1$$

where k and c is any natural number.

3. Dec 1, 2005

### Galileo

Using contradiction (indirect proof), you can assume either m or n to be even (that is, a multiple of two) and show that mn must also be even.

4. Dec 1, 2005

### HallsofIvy

Staff Emeritus
No, that's exactly the wrong thing to do.

Since blimkie wants to use indirect proof to prove that "both m and n must be odd, he should negate that: "either m or n is even".

So assume m= 2p, which is even for any integer p, multiply by n and see what happens!

Last edited: Dec 4, 2005
5. Dec 1, 2005

### vaishakh

A number to be even it should be divisible by 2. thus for the product mn to be divisible by 2 any of the integers m or n must be divisible by prime 2. thus the divisibility testdiectlygives you the answer that then anyone of them must be an even number.