1. Give an interpretation of the equivalence classes for the equivalence relation R in: Let R be the relation on the set of ordered pairs of positive integers such that ((a,b),(c,d)) ℇ R if and only if ad = bc.

2) suppose that R1 and R2 are equivalence relations on the set S. Determine whether each of these combinations of R1 and R2 must be an equivalence relation.

a) R1 U R2

b) R1 ∩ R2

c) R1 ⊕ R2

3) Do we necessarily get an equivalence relation when we form the symmetric closure of the reflexive closure of the transitive closure of a relation?

4) Give an example of an infinite lattice with both a least and a greatest element.

Thank You