In the following problems you will fill in the details for

Last updated: 10/28/2023

In the following problems you will fill in the details for various proofs On exams you are expected to write out the entire proof so you should practice by writing out the proof of each statement then comparing your work with the proofs given in the problem set In this problem you will complete the details of the proof of a direct proof Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer If n is odd then n 5n is even Proof Suppose that n is odd By definition n 2k 1 for some integer k So n 5n 2k 1 5 2k 1 2m where m Since Z is closed under addition and multiplication me Z Since n 5n 2m this means that n 5n is even