Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.

Question

Philoid · Accepted Answer

Given: n(A) = 3 and n(B) = 2 and If (x, 1), (y, 2), (z, 1) are in A × B.

By definition of Cartesian product of two non-empty Set P and Q:

P × Q = {(p, q): p Є P, q Є Q}

Hence, we see P = set of all first elements.

Q = set of all second elements.

⇒ (x, y, z) are elements of A and (1,2) are elements of B.

⇒ As n(A) = 3 and n(B) = 2 so, A = {x, y, z} and B = {1, 2}.