Question

If A × A has 16 elements, S = {(a, b) ∈ A × A : a < b} ; (−1, 2) and (0, 1) are two elements of S, then find the remaining elements of S

Answer 1

Given A × A has 16 elements.

∴ A has 4 elements.

Also S = {(a, b) ∈ A × A: a < b}

Given (−1, 2) and (0, 1) ∈ S

A = {−1, 0, 1, 2}

The elements of S are

S = {(−1, 0), (−1, 1), (−1, 2), (0, 1), (0, 2), (1, 2)}

∴ The other elements of the sets are

((− 1, 0), (− 1, 1), (0, 2), (1, 2)}