Question

If n(A)=15;n(AnB)=8 and n(AuB)=19 then find the value of n(B).​

Answer 1

SOLUTION

GIVEN

n(A) = 15 , n(A ∩ B) = 8 and n(A ∪ B ) = 19

TO DETERMINE

The value of n(B)

EVALUATION

Here it is given that

n(A) = 15 , n(A ∩ B) = 8 and n( A ∪ B ) = 19

We are aware of the formula on set theory that

n( A ∪ B ) = n(A) + n(B) - n(A ∩ B)

⇒ 19 = 15 + n(B) - 8

⇒ n(B) = 19 - 15 + 8

⇒ n(B) = 12

FINAL ANSWER

Hence the required value n(B) = 12

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