Answer to Question #143319 in Discrete Mathematics for Christine Joy Sato

Question

“The product of two odd numbers is odd.”
Using Direct proof method

Answer 1

If n and m are odd then n.m is odd,

n,m are real numbers

n=2a+1,

m=2b+1,

n.m=(2a+1).(2b+1),

n.m=4ab+2a+2b+1,

n.m=2(2ab+a+b)+1.

Odd integer=2k+1.

Multiply terms

Factor out of 2

n.m=2k+1, where

k=2ab+a+b=integer,

n.m are odd.