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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.

Q9  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 \times B, find A and B, where x, y and z are distinct elements.

Answers (1)
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It is given that
 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 \times Q = \left \{ (p,q) : p \ \epsilon \ P , q \ \epsilon \ Q \right \}
Now, we can see that
P = set of all first elements.
And 
Q = set of all second elements.
Now,
\Rightarrow (x, y, z) are elements of A and (1,2) are elements of B
 As n(A) = 3 and n(B) = 2
Therefore,
A = {x, y, z} and B = {1, 2}

 

 

 

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