Suppose x and y are odd. Prove xy odd.

Question

Hint: an odd number can be written as 2m + 1, where n is an interger

Answer 1

QUESTION: Suppose x and y are odd. Prove xy odd.

Hint: an odd number can be written as 2m + 1, where n is an interger.

Let x = 2m+1

Let y = 2n+1

Then xy = (2m + 1)(2n + 1) = 4mn + 2(m+n) + 1 = 2(2mn+m+n) + 1 = 2k + 1 = odd number