Question:

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

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