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.