Use the union rule to answer the question.

If n(B) = 52, n(A ∩ B) = 15 and n(A U B) = 86, what is n(A)?

**Solution:-**

Recall that the union rule for sets states that

n(A U B) = n(A ) + n(B) – n(A ∩B)

for any finite set A and B. To find n(A), substitute each of the given quantities into the union rule. Then, solve for n(A).

Substitute the given values of n(B), n(A ∩ B), and n(A U B) into the union rule.

n(A U B) = n(A) + n(B) – n(A ∩ B)

86 = n(A) + 52 – 15

Now, solve for n(A).

86 = n(A ) + 52 – 15

49 = n(A)