UGC NET CSE | December 2019 | Part 2 | Question: 3

Question

The Boolean expression $AB+A \overline{B}+\overline{A}C+AC$ is unaffected by the value of the Boolean variable _________.

• A. $A$
• B. $B$
• C. $C$
• D. $A, B$ and $C$

Answer 1

Let us simplify the given boolean expression:$AB+A\overline B+\overline AC+AC$

$=A(B+\overline B)+(\overline A+A)C$

$=A.1+1.C$

$=A+C$

So the output doesn’t depend on the value of B.

So option B is the correct answer.

Answer 2

B is the correct option.

You just have to simplify this expression. It will result in A+C.

Answer 3

The answer is b)

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

A+C                            (we know that  B+B'=1 and A+A'=1)


The Boolean expression AB+AB'+A'C+AC is unaffected by the value of the Boolean variable B.

Answer 4

Whenever this type of boolean expression come simply focus to take common out of it:

=AB+AB’+A’C+AC

=A(B+B’)+C(A+A’)

=A+C  (As we know 0+1=1)

So from here we can see expression is independent from B.

So, answer is B.