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