1. [6 pts] Let R1 be the relation defined on the set of ordered pairs of positive integers such that (a,b)R1(c,d) if and only if ad=bc. Is R1 an equivalence relation? Prove your answer. 2. [6 pts] Let R1 and R2 be two equivalence relations. Is R1R2 an equivalence relation? Prove your answer. 3. [6 pts] Binary relation R over set A is called circular if for every a,b,cA, ((a,b)R(b,c)R)(c,a)R. Prove or disprove the following claim: R is an equivalence relation if and only if R is reflexive and circular. 4. [6 pts] Give a partially ordered set, or poset, that has 1. a minimal element but no maximal element. 2. neither a maximal nor a minimal element. 5. [6 pts] Let (A,) be a partially ordered set that has no minimal element and A is not empty. Can A be finite? Prove your