First slide

Operations 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 $B \times A$ are

Easy

A

$2^{99}$
B

$99^{2}$
C

$100$
D

$18$

Solution

$n (A \times B) \cap (B \times A)$
$= n ((A \cap B) \times (B \cap A)) = n (A \cap B) . n (B \cap A)$
$= n (A \cap B) . (A \cap B) = (99) (99) = 99^{2} .$

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