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ISI2017-DCG-10

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$(A'BC')'+(AB'C)'\\=\left\{(A')'+B'+(C')'\right\}+\left\{A'+(B')'+C'\right\};~[\text{Applying De Morgan's law}]\\=A+B'+C+A'+B+C';~[\because (X')'=X]\\=(A+A')+(B+B')+(C+C');~[\text{Commutative and Associtive laws}]\\=1+1+1;~[\because X+X'=1 \text{ as the Complement law}]\\=1;~[\because 1+1=1 \text{ in Boolean algebra}]$

 

So the correct answer is B.

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Answer : B

(A′BC′)′+(AB′C)′  =>     (A+B'+C) + (A'+B+C')

(A+A')+(B+B')+(C+C') = 1
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