GATE CSE 1989 | Question: 5-a

Question

Find values of Boolean variables $A, B, C$ which satisfy the following equations:

• A+ B = 1
• AC = BC
• A + C = 1
• AB = 0

Comments

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Answer 1

From $A+B=1$ and $AB=0$ we get either of $A,B$ is $1$ and another is $0$

Now, $AC=BC$, here $C$ has to be $0$ (because $A,B$ has different values)

$C=0$

Now, $A+C=1$

So, $A=1$ and $AB=0$ so, $B=0$

So, we get:

$A=1$ , $B=0$ , $C=0$

These are the values.

Comments

Sorry, it is AC = BC.

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@vipin But its still not satisfying AC=BC

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so we get :-
A = 1, B = 0, C = 0
 

• A+ B = 1       --» 1+0 = 1
• AC = BC       --» 1*0 = 1*0
• A + C = 1       --» 1+0 = 1
• AB = 0           --» 1*0 = 0

Answer 2

The value of Boolean variables A,B,C {1,0,0}

Comments

this is also a easy way

Answer 3

Looking at first and third arguments, we can satisfy both by putting A =1 and B and C to 0 , now it can be easily checked that other constraints are still true.