In this problem you will complete the details of the proof

Last updated: 10/28/2023

In this problem you will complete the details of the proof of an indirect proof Fill in the blanks below Each blank should be filled with a polynomial involving the variables k and p Prove Let m n be integers If mn is even then m is even or n is even Proof Suppose that mn is even Assume for the sake of contradiction that it s not true that m is even or n is even By DeMorgan s Law this means that m is odd and n is odd By definition of odd m 2k 1 and n 2p 1 for some integers k and p This means that mn 2k 1 2p 1 2N 1 where N Since Z is closed under addition and multiplication NE Z Since mn 2N 1 this means that mn is odd This contradicts the fact that mn is even Therefore it must be true that m is even or n is even O