Answers must be correct. Or else it will be flagged. All sub-parts need to be answered with step by step process showing all work and reasoning.

YOU MUST PROVIDE ALL ANSWERS AS PER THE QUESTIONS.

DON'T PROVIDE WRONG ANSWERS AND DON'T ANSWER IF YOU DON'T WANT TO ANSWER ALL SUB-PARTS. INCOMPLETE ANSWERS WILL BE FLAGGED

DISCRETE STRUCTURES

Question 2 (24 points) Prove the following statements. a) Let x, y E Z. Then ry is odd if and only if x is odd and y s odd. b) Let r, y ? R. Then (z + y)2-2,2 + ?? if and only if r-0 or y-0. c) Let a,DE N. Then a-: gcd(a, b) if and only if alb. and only if x- U or-0