Question

find the number of tripalets (a,b,c) where a, b ,c are subsats of {1,2,3,...,8} such that a intersection b intersection c=fai ,a intersection b is not equal to fai or bintersection c is not equal fai .​

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If the universal set U={1,2,3,4,5,6,7},A={1,2,5,7},B={3,4,5,6}. Verify (A∪B)

′

=A

′

∩B

′

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Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B)

′

=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}

=ϕ

A

′

∩B

′

=(U−A)n(U−B)

={3,4,6}n{1,2,7}

=ϕ

Hence (A∪B)

′

=A

′

∩B

′

.