Answer:
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)}
Step-by-step explanation:
Given sets,
A = {1, 2, 3, 4, 5} and B = {0, 1, 2, 3, 4},
a) If R = {(a, b) | a + b = 5} 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) | 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) | 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)}
