# Thread: proof by contraposition help

1. ## proof by contraposition help

1. m is an integer. Prove by contraposition that if 5m + 4 is odd then m is odd
2. suppose m is even, than

m = 2n for some n in N

so

5(2n) +4 = 20n+4

factor out 2 = 2(10n+2)

which is even, have i proved this ? ]

2. ## Re: proof by contraposition help

Originally Posted by Tweety
1. m is an integer. Prove by contraposition that if 5m + 4 is odd then m is odd
2. suppose m is even, than

m = 2n for some n in N

so

5(2n) +4 = 20n+4

factor out 2 = 2(10n+2)

which is even, have i proved this ? ]
Yep. A=5m+4 is odd, B=m is odd, show ~B --> ~A which is what you did.