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  4. Given n(U)=20,n(A)=12,n(B)=9, n(A∩ B)=4, where U is the universal set, A and B are subsets of U then n[(A∪ B)c] equals to:

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Q. 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}] $ equals to:

KEAMKEAM 2004Sets

Solution:

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