Refer to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations R and S from A to B, R ∪ S = {(x, y) ∈ A × B | (x, y) ∈ R or (x, y) ∈ S}
R ∩ S = {(x, y) ∈ A × B | (x, y) ∈ R and (x, y) ∈ S}.

Exercise

Let A = { –1, 1, 2, 4} and B = {1, 2} and define relations R and S from A to B as follows: For all (x, y) ∈ A × B,
x R y ⇔ |x | = |y| and
x S y ⇔ x – y is even.

Required:
State explicitly which ordered pairs are in A × B, R, S, R ∪ S, and R ∩ S.