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+15 votes

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

  • A+ B = 1
  • AC = BC
  • A + C = 1
  • AB = 0
in Digital Logic by Boss (30.7k points)
edited by | 646 views

5 Answers

+17 votes
Best answer
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)


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.
by Boss (18k points)
edited by
Can A=1 B=0 C=1 be also be an answer?
@vipin Does AB = AC condition satisfying? When you are taking A = 1 B = 0 and C = 1.
There is no such condition AB=AC
Sorry, it is AC = BC.
+5 votes

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

by Loyal (8.7k points)
this is also a easy way
–1 vote

A=1 B=0 And  C=0

by Active (2k points)
–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.
by (171 points)
–1 vote

think without ink ..!

A = 1

B= 0

C= 0

by Active (4.6k points)

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