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Question

If the number of elements in each of universal set, set A and set B are represented as n(U), n(A), n(B) respectively, then the number of elements that are not in set A and not in set B is given by ___.


A

n(AUB)

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B

n(AB)

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C

n(U)n(AB)

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D

n(U)n(AB)

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Solution

The correct option is D

n(U)n(AB)


The elements that are not in set A and not in set B belong to the set AB.

But by de-Morgan's law for complementation, we have
AB=(AB).
Thus, n(AB)=n((AB)) =n(U)n(AB).


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