Sets-Relations-And-Functions Question 153

Question: Given $ n(U)=20,n(A)=12,n(B)=9,n(A\cap B)=4, $ where U is the universal set, A and B are subsets of U, then $ n({{(A\cup B)}^{c}})= $

Options:

A) 17

B) 9

C) 11

D) 3

Show Answer

Answer:

Correct Answer: D

Solution:

  • [d] $ n(A\cup B)=n(A)+n(B)-n(A\cap B) $ $ =12+9-4=17 $ Now, $ n({{(A\cup B)}^{c}})=n(U)-n(A\cup B) $ $ =20-17=3 $

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