ISRO2015-5

Question

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

• A. $(\overline{\text{A}} + \overline{\text{B}})+(\text{B} + \overline{\text{C}}). (\overline{\text{A}} + \overline{\text{C}})$
• B. $(\overline{\text{A}} . \overline{\text{B}})+(\text{B} \overline{\text{C}}+\overline{\text{A}}\; \overline{\text{C}})$
• C. $(\overline{\text{A}} + \overline{\text{B}}).(\text{B}+\overline{\text{C}})+ (\text{A}+ \overline{\text{C}})$
• D. $\text{(A+B)} . (\overline{\text{B}}+\text{C) (A+C)}$

Answer 1

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

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

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

Answer 2

Answer : A

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

Answer 3

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

Answer 4

answer - (A)

convert AND to OR

complement uncomplemented terms and vice-versa