First slide

Introduction to Relations (XI) on Sets

Question

If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets $A \times B and B \times A is$

Moderate

A

$2^{99}$
B

$99^{2}$
C

100
D

18

Solution

$\begin{array}{l} n ((A \times B) \cap (B \times A)) \\ = n ((A \cap B) \times (B \cap A)) = n (A \cap B) \cdot n (B \cap A) \\ = n (A \cap B) \cdot n (A \cap B) = (99) (99) = 99^{2} \end{array}$

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