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The complement of the Boolean expression $AB(\bar{B}C+AC)$ is

1. $(\bar{A} + \bar{B})+(B + \bar{C}). (\bar{A} + \bar{C})$
2. $(\bar{A} . \bar{B})+(B \bar{C}+\bar{A} \bar{C})$
3. $(\bar{A} + \bar{B}).(B+\bar{C})+ (A+ \bar{C})$
4. $(A+B) . (\bar{B}+C) (A+C)$

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$\overline{ AB(\bar{B}C+AC) }$=$\overline{ AB}+(\overline{\bar{B}C})(\overline{AC} )$

$(\bar{ A}+\bar{B})+(B+\bar{C})(\bar{A}+\bar{C} )$

Hence,Option (A)$(\bar{ A}+\bar{B})+(B+\bar{C})(\bar{A}+\bar{C} )$ is the correct choice.

by Boss (41.2k points)
selected by

Expression : AB(B'C + AC)

Complement of it is [AB(B'C + AC)]'

(AB)' + (B'C + AC)'   // Demorgan's law

(AB)' + (B'C)' (AC)'

(A' + B') + (B+C') (A'+C')  // Demorgan's law

by Boss (45.4k points)
+1 vote
Given that

F = AB (B'C + AC)
Now find F' = ?

F' = (AB(B'C + AC))'
F' = (AB)' + (B'C + AC )'        (Using Demorgan's Law :(AB)' = A' + B'
F' = (A' + B') + (B'C)'.(AC)'     (Again Using Demorgan's Law)
F' = (A' + B') + (B + C').(A' + C')        (Again using Demorgan's Law)

So Option (A) is a correct answer
by Veteran (59k points)

convert AND to OR

complement uncomplemented terms and vice-versa
by Loyal (9.9k points)
option A
by Active (1.3k points)