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