Let R = {(a, b) : a, b ϵ Z and b = 2a – 4}. If (a, –2} ϵ R and (4, b²) ϵ R. Then, write the values of a and b.

Let R = {(a, b) : a, b ϵ Z and (a – b) is even}.

Then, show that R is an equivalence relation on Z.

Let A = {1, 2, 3} and R = {(a, b) : a, b ϵ A and |a² – b²| ≤ 5.

Write R as a set of ordered pairs.

Mention whether R is (i) reflexive (ii) symmetric (iii) transitive. Give reason in each case.

Let R be a relation on Z, defined by (x, y) ϵ R ↔ x² + y² = 9. Then, write R as a set of ordered pairs. What is its domain?

Let A be the set of first five natural numbers and let R be a relation on A, defined by (x, y) ϵ R ↔ x ≤ y.

Express R and R^–1 as sets of ordered pairs.

Find: dom (R^–1) and range (R).