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2.Relations and Functions
hard
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
A
${2^{99}}$
B
${99^2}$
C
$100$
D
$18$
Solution
(b) $n((A \times B) \cap (B \times A))$
$ = n((A \cap B) \times (B \cap A)) = n(A \cap B).n(B \cap A)$
$ = n(A \cap B).n(A \cap B) = (99)(99) = {99^2}$.
Standard 11
Mathematics
