If A = {1, 2, 3, 4, dots, 100} and B = {51, 5 | vedclass

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(C) The set $A$ contains elements from $1$ to $100$,so $n(A) = 100$.The set $B$ contains elements from $51$ to $180$,so $n(B) = 180 - 51 + 1 = 130$.Th

Vedclass · Accepted Answer

$2500$

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(C) The set $A$ contains elements from $1$ to $100$,so $n(A) = 100$.The set $B$ contains elements from $51$ to $180$,so $n(B) = 180 - 51 + 1 = 130$.The intersection $A \cap B$ contains elements from $51$ to $100$,so $n(A \cap B) = 100 - 51 + 1 = 50$.We know that $(A 	imes B) \cap (B 	imes A) = (A \cap B) 	imes (B \cap A)$.Therefore,the number of elements is $n((A \cap B) 	imes (B \cap A)) = n(A \cap B) 	imes n(B \cap A)$.Since $n(A \cap B) = 50$,we have $50 	imes 50 = 2500$.

If $A = \{1, 2, 3, 4, \dots, 100\}$ and $B = \{51, 52, 53, \dots, 180\}$,then the number of elements in $(A \times B) \cap (B \times A)$ is:

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