If n(A) denotes the number of elements in set A and if n(A) = 4, n(B) = 5 and n(A ? B) = 3, then n[(A × B) ? (B × A)] =

Question

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

Smart Achievers · Accepted Answer

(2)

Given $n (A) = 4, n (B) = 5, n (A \cap B) = 3$

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

$= n (A \cap B) \times n (B \cap A) = 3 \times 3 = 9$ $[∵ n (A \times B) = n (A) \times n (B)]$

Solution

Q.
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 $n [(A \times B) \cap (B \times A)] =$

1 8

2 9

3 10

4 11

Ans.
(2)

Given $n (A) = 4, n (B) = 5, n (A \cap B) = 3$

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

$= n (A \cap B) \times n (B \cap A) = 3 \times 3 = 9$ $[∵ n (A \times B) = n (A) \times n (B)]$

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