# ISI2017-DCG-10

311 views

The value of the Boolean expression (with usual definitions) $(A’BC’)’ +(AB’C)’$ is

1. $0$
2. $1$
3. $A$
4. $BC$

recategorized

$(A'BC')'+(AB'C)'\\=\left\{(A')'+B'+(C')'\right\}+\left\{A'+(B')'+C'\right\};~[\text{Applying De Morgan's law}]\\=A+B'+C+A'+B+C';~[\because (X')'=X]\\=(A+A')+(B+B')+(C+C');~[\text{Commutative and Associtive laws}]\\=1+1+1;~[\because X+X'=1 \text{ as the Complement law}]\\=1;~[\because 1+1=1 \text{ in Boolean algebra}]$

So the correct answer is B.

edited

Option B) 1

Given $(A’BC’)’ +(AB’C)’$

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

$1$

(A′BC′)′+(AB′C)′  =>     (A+B'+C) + (A'+B+C')

(A+A')+(B+B')+(C+C') = 1
(A´BC´)´+(AB´C)´=(A´BC´AB´C)´=0´=1 ( By De Morgan theorem)

## Related questions

1 vote
1
114 views
The value of $\dfrac{1}{\log_2 n}+ \dfrac{1}{\log_3 n}+\dfrac{1}{\log_4 n}+ \dots + \dfrac{1}{\log_{2017} n}\:\:($ where $n=2017!)$ is $1$ $2$ $2017$ none of these
The area of the shaded region in the following figure (all the arcs are circular) is $\pi$ $2 \pi$ $3 \pi$ $\frac{9}{8} \pi$
If $2f(x)-3f(\frac{1}{x})=x^2 \: (x \neq0)$, then $f(2)$ is $\frac{2}{3}$ $– \frac{3}{2}$ $– \frac{7}{4}$ $\frac{5}{4}$
If $A$ is a $3 \times 3$ matrix satisfying $A^3 – A^2 +A-I= O$ (where $O$ is the zero matrix and $I$ is the identity matrix) then the value of $A^4$ is $A$ $O$ $I$ none of these