Test by Bikram | Mock GATE | Test 1 | Question: 22

Question

For the  Boolean equation  $AB +$ $\sim AC$$= 1$,  $AC +B =  0$,  the value of  $A$, $B$ and $C$ will be:

• A. $0$, $0$,$1$
• B. $1$,$1$,$0$
• C. $0$,$1$,$0$
• D. $1$,$0$,$0$

Answer 1

Answer is option a.

 AB + ~AC = 1................(1)

 AC +B =  0....................(2)

Now substitute A=0,B=0,C=1 in equation(1) & (2)

From equation (1)

0.0+1.1=1

1=1

LHS=RHS

hence true.

From equation (2)

0.1+0=0

0=0

LHS=RHS

hence true.

Comments

1,0,0 also gives same result?

---

1,0,0 will not satisfy the equation  AB + ~AC = 1

On LHS

=1*0+0*0

=0

But RHS is 1

Hence LHS is not equal to RHS

Answer 2

an answer would be  "A" if we consider only "A" complement not the whole complement of (AC) 

Comments

No,

option D  1,0,0 will not satisfy that given equation, see above comment please.