2. Let R be a relation defined on the set of integers Z where a Rb if and only if a? = b° (mod 5). Determine whether R is an equivalence relation.

Consider the relation R on Z with rule (a, b) in R iff a + 2b is even. Is R reflexive, symmetric, transitive?

3. Define a relation on the real numbers as follows: x Ry if and only if x² + y² = 1. Determine if R is reflexive, symmetric, and/or transitive. For each property, give sufficient justification for your answer.

Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c,d)) = R if and only if ad = bc. Show R is an equivalence relation.

8. Let A be a set of nonzero integers and let R be a relation on A × A defined by (a, b)R(c, d) whenever ad = bc. Show that R is an equivalence relation. That is, R is reflexive, symmetric, and transitive.