If A = {1, 2, 3, 4, ..., 100} and B = {51, 52 | vedclass

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(C) Given sets are $A = \{1, 2, 3, ..., 100\}$ and $B = \{51, 52, 53, ..., 180\}$.First,find the intersection of sets $A$ and $B$: $A \cap B = \{51, 5

Vedclass · Accepted Answer

$2500$

Vedclass · Answer

(C) Given sets are $A = \{1, 2, 3, ..., 100\}$ and $B = \{51, 52, 53, ..., 180\}$.First,find the intersection of sets $A$ and $B$: $A \cap B = \{51, 52, 53, ..., 100\}$.The number of elements in $A \cap B$ is $n(A \cap B) = 100 - 51 + 1 = 50$.We know that $(A 	imes B) \cap (B 	imes A) = (A \cap B) 	imes (B \cap A)$.Since $(A \cap B) = (B \cap A)$,we have $(A \cap B) 	imes (A \cap B)$.The number of elements is $n((A 	imes B) \cap (B 	imes A)) = n(A \cap B) 	imes n(B \cap A) = 50 	imes 50 = 2500$.

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

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