# GATE1989-5-a

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

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

edited

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.

edited
0
Can A=1 B=0 C=1 be also be an answer?
0
@vipin Does AB = AC condition satisfying? When you are taking A = 1 B = 0 and C = 1.
0
There is no such condition AB=AC
0
Sorry, it is AC = BC.

The value of Boolean variables A,B,C {1,0,0} 0
this is also a easy way
–1 vote

A=1 B=0 And  C=0

–1 vote
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.
–1 vote

think without ink ..!

A = 1

B= 0

C= 0

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