Question

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

Answer 1

Given, A and B are two sets such that n(A) = 3 and n(B) = 2.
then, number of elements in A × B = n(A) × n(B)
= 3 × 2 = 6

A/C to question, A × B contains (x, 1), (y, 2), (z, 1)

we know, in A × B, A is the set of all first elements and B is the set of all 2nd elements.

so, A = {x , y, z} [since first element contains x , y and z]

and B = {1, 2} [ since 2nd element contains 1 and 2 ]


hence, A = {x , y, z} and y = {1, 2}

Answer 2

ANSWER

It is given that 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 ordered pair elements of A×B

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

Since n(A)=3 and n(B)=2 it is clear that A={x,y,z} and B={1,2}