Question

n(A)=36,n(B)=10,n(AuB)=40,n(A') =27,find n(ANB) and n(U)​

Answer 1

SOLUTION

GIVEN

n(A) = 36 , n(B) = 10 , n(A∪B)=40 , n(A') = 27

TO DETERMINE

n(A∩B) and n(U)

EVALUATION

Here it is given that

n(A) = 36 , n(B) = 10 , n(A∪B)=40 , n(A') = 27

n(A') =27 gives

n(U) - n(A) = 27

⇒ n(U) = 36 + 27

∴ n(U) = 63

Again n(A∪B) = 40 gives

n(A) + n(B) - n(A∩B) = 40

⇒ 36 + 10 - n(A∩B) = 40

⇒ n(A∩B) = 46 - 40

⇒ n(A∩B) = 6

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Answer 2

SOLUTION

GIVEN

n(A) = 36 , n(B) = 10 , n(A∪B)=40 , n(A') = 27

TO DETERMINE

n(A∩B) and n(U)

EVALUATION

Here it is given that

n(A) = 36 , n(B) = 10 , n(A∪B)=40 , n(A') = 27

n(A') =27 gives

n(U) - n(A) = 27

⇒ n(U) = 36 + 27

∴ n(U) = 63

Again n(A∪B) = 40 gives

n(A) + n(B) - n(A∩B) = 40

⇒ 36 + 10 - n(A∩B) = 40

⇒ n(A∩B) = 46 - 40

⇒ n(A∩B) = 6

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