If $n (A)$ denotes the number of elements in set $A$ and if $n (A) = 4, n (B) = 5$ and $n (A \cap B) = 3$ then $n [(A \times B) \cap (B \times A)]$ is

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Solution

n(A) =4, n (B) =5
$n (A \cap B) = 3$
$n [(A \times B) \cap (B \times A)] = n [(A \cap B) \times (B \cap A)]$
$= n (A \cap B) \times n (B \cap A)$
$= 3 \times 3 = 9$

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Similar questions

If A and B are two sets having 3 elements in common. If n(A) = 5 and n(B) = 4, find $n [(A \times B)$ and $n (A \times B) \cap (B \times A)]$ .

A, B

A \cup B = (A - B) \cup (B - A) \cup (A \cap B)

n (A \cup B) = n (A) + n (B) - n (A \cap B)

n (A)

A

n ((A \times B) \cap (B \times A)] =

3

n (A) = 5, n (B) = 4

n (A \times B)

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