If two sets A and B have 99 elements in commo | vedclass

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Question

(B) Let $C = A \cap B$. Given that the number of elements in $C$ is $n(C) = 99$.An element $(x, y)$ belongs to $A 	imes B$ if $x \in A$ and $y \in B$

Vedclass · Accepted Answer

$(99)^2$

Vedclass · Answer

(B) Let $C = A \cap B$. Given that the number of elements in $C$ is $n(C) = 99$.An element $(x, y)$ belongs to $A 	imes B$ if $x \in A$ and $y \in B$.An element $(x, y)$ belongs to $B 	imes A$ if $x \in B$ and $y \in A$.For an element $(x, y)$ to be in both $A 	imes B$ and $B 	imes A$,we must have $x \in A \cap B$ and $y \in A \cap B$.Thus,$(x, y) \in (A \cap B) 	imes (A \cap B)$.The number of such elements is $n(A \cap B) 	imes n(A \cap B) = 99 	imes 99 = (99)^2$.

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

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