## 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

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.​

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1 month 2021-09-16T15:37:33+00:00 2 Answers 1 views 0

1. 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 × B

B = Set of second elements of the ordered pair elements of A × B.

So,

clearly x, y, and z are the elements of A; and

clearly 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}.

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}.