## 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 distinc

Question

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

## Answers ( )

Given,n(A) = 3 and n(B) = 2; and (x, 1), (y, 2), (z, 1) are in A × B.We know that,A = Set of first elements of the ordered pair elements of A × BB = Set of second elements of the ordered pair elements of A × B.So,clearly x, y, and z are the elements of A; andclearly x, y, and z are the elements of A; and1 and 2 are the elements of B.As n(A) = 3 and n(B) = 2,it is clear that set A = {x, y, z} and set B = {1, 2}.Given, A and B are two sets such that n(A) = 3 and n(B) = 2.

(x, 1), (y, 2) and (z, 1) ∈ A × B.

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

∴ x, y and z are elements of A and 1, 2 are elements of B.

Now, n(A × B) = n (A) × n(B) = 3 × 2 = 6

So, A = {x, y, z} and B = {1, 2}.