CS 151: Homework 4 Due March 8th, 8:00pm on Gradescope 1 Relations a) Suppose R is a symmetric relation over set A. Prove or disprove that R2 is symmetric. b) Suppose R and S are transitive relations over set A. Prove or disprove that SR is transitive. c) Consider the following relation R over the integers (Z).R={(a,b)Z2:kZa=kb}. (a) Prove or disprove whether R is reflexive (b) Prove or disprove whether R is symmetric (c) Prove or disprove whether R is anti-symmetric (d) Prove or disprove whether R is transitive