The complement of the Boolean expression AB ( B'C + AC ) is , ISRO 2015

2015

The complement of the Boolean expression AB ( B'C + AC ) is , ISRO 2015

  1. A.

    ( A' + B' ) + ( B + C' )( A' + C' )

  2. B.

    ( A' + B' ) + ( BC' + A'C' )

  3. C.

    ( A' + B' )( B + C') + ( A + C' )

  4. D.

    ( A + B )( B' + C )( A + C )

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Correct answer: A

First, simplify the Boolean expression AB(B'C + AC). Distributing AB gives ABB'C + ABAC. Since B'B = 0, the first term becomes 0. The second term simplifies to ABC because AA = A. Thus, the expression reduces to ABC. To find the complement, apply De Morgan's Law: (ABC)' = A' + B' + C'. Therefore, the complement of the given expression is A' + B' + C'.

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