Question

Let A = {1, 2, 3, 4, 5} and B = {0, 1, 2, 3, 4}.

a) List all the ordered pairs in the relation R = a + b = 5 on A.

b) List all the ordered pairs in the relation R = (a, b) on A.

c) List all the ordered pairs in the relation R = a < b from A to B.

Answer 1

a) R = {(1, 4), (2, 3)}

b) R = {(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)}

c) R = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

Explanation:

Given sets,

A = {1, 2, 3, 4, 5} and B = {0, 1, 2, 3, 4},

a) If R = (a, b) is the relation on A,

That is, a, b ∈ A

∵ 1 + 4 = 5,

and 2 + 3 = 5,

Thus, R = {(1, 4), (2, 3)}

b) If R = (a, b) is the relation on A,

That is, a, b ∈ A

∵ 1 < 2, 1 < 3, 1 < 4, 1 < 5, 2 < 3, 2 < 4, 2 < 5, 3 < 4, 3 < 5 and 4 < 5,

Thus, R = {(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)}

c) If R = (a, b) is the relation from A to B,

That is, a ∈ A, b ∈ B,

∵ 1 < 2, 1 < 3, 1 < 4, 2 < 3, 2 < 4 and 3 < 4

Thus, R = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}