Question

If n(A – B) = 30, n(A ∪ B) = 65 and n(A ∩ B) = 22, then find n(B).

please solve this I will mark 5 stars if its correct

Answer 1

n(B) = 45

Explanation:

n(A U B) = 65 size of all elements in set A or set B or both

n(A ∩ B) = 22 size of all elements common to sets A and B

n(A - B) = 30 size of all elements in set A but not set B

n(A) = n(A - B) + n(A ∩ B) the total number of elements in set A is the

the number of elements in A but not B plus

the number of elements common to A and B
= 30 + 22 = 52

n(AUB) = n(A) + n(B) - n(A∩B)

So n(B) = n(AUB) - n(A) + n(A∩B)

= 65 - 52 + 22

= 45