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Number of Elements in a Cartesian Product

If A AND B AR...

Question

If A AND B ARE SUBSETS OF X:
n(X)=50
n(A)=35
n(B)=20
n(AUB)=5
FIND A) n(A INTERSECTING B)
B)

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Solution

$The number of elements in the union of two sets is given by the formula : n (A \cup B) = n (A) + n (B) - n (A \cap B) This implies that the number of elements in intersection of two sets is given by, n (A \cap B) = n (A) + n (B) - n (A \cup B) Put the values n (A) = 35, n (B) = 20, n (A \cup B) = 5 to get, n (A \cap B) = 35 + 20 - 5 n (A \cap B) = 55 - 5 n (A \cap B) = 50$

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