Assignment:
Q1. Consider the partial order less than or equal to(<=) on the set X of positive integers given by "is a divsor of." Let a and b be two integers. Let c be the largest integer such that c<=a and c<=b and let d be the smallest integer such that a<=d and b<=d. What are c and d?
Q2. Prove that the intersection of R and S of two equivalence relations R and S on a set X is also an equivalence relation on X. Is the union of two equivalence relations on X always an equivalence relation?
Provide complete and step by step solution for the question and show calculations and use formulas.