Let A = {1, 2, 3, 4} and R = {(a, b): a ∈ A, b ∈ A, a divides b}. Write R explicitly.
given: A = {1, 2, 3, 4} and R = {(a, b): a ∈ A, b ∈ A, a divides b}
To find: set R
Both elements of R, a and b, belongs to set A and relation between and elements a and b is that a divides b
So,
1 divides 1, 2, 3 and 4.
2 divides 2 and 4.
3 divides 3.
4 divides 4.
∴ R = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 4), (3, 3), (4, 4)}