Question

If n(U) = 40, n(A´) = 12, n(B´) = 18 and n(A ∩ B) = 20 then n(A ∪ B), where U is the universal set, is

Answer 1

Answer:

n(U) = 40

n(A) = n(U) - n(A') = 40-12 = 28

n(B) = n(U) - n(B') = 40-18 = 22

n(A intersection B) = 20

n(AUB) = n(A) + n(B) - n(A ∩ B)

= 28+22-20

=30

Answer 2

n(A ∪ B) = 30

Given,

n(U) = 40

n(A') = 12

n(B') = 18

n(A∩B) = 20

To Find,

n(A∪B)=?

Solution,

We have been given that the number of elements in the universal set is 40

Also, the number of elements in the complement of set A is 12.

Therefore, the number of elements in the set A, n(A) = n(U) - n(A') = 40 - 12 = 28.

And, the number of elements in the complement of set B is 18.

Therefore, the number of elements in the set B, n(B) = n(U) - n(B') = 40 - 18 = 22.

Also, we have been given that n(A∩B) = 20

We can use a simple formula to find the number of elements in the union of A and B, n(A∪B) = n(A) + n(B) - n(A∩B)

⇒ n(A∪B) = 28 + 22 - 20

⇒ n(A∪B) = 50 - 20

⇒ n(A∪B) = 30

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