Suppose x and y are odd prove xy is odd?

Answer 1

Write x and y in terms of integers, which we call a and b. For some integer,

x = 2a + 1

y = 2b + 1

Multiplying them, you get:

xy = (2a+1)(2b+1) = 4ab + 2a + 2b + 1

Since the first terms are even, adding one makes the final result odd.