Let X be the universal set for sets A and B. If n(A)=200,n(B)=300 and n(A∩B)=100, then nA′∩B′ is equal to 300 provided n(X) is equal to

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600

700

800

900

answer is B.

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Detailed Solution

Given n(A)=200,n(B)=300 and n(A∩B)=100we know thatn(A∪B)=n(A)+n(B)−n(A∩B)n(A∪B)=200+300−100=400Also, nA′∩B′=n(A∪B)′=n(X)−n(A∪B)⇒300=n(X)−400⇒n(X)=700

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