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  1. Let $\ast$ be a Boolean operation defined as $A\ast B = AB + \overline{A}\;\overline{B}$. If $C=A\ast B$ then evaluate and fill in the blanks:
    1. $A\ast A=$______
    2. $C\ast A=$______
  2. Solve the following boolean equations for the values of $A, B$ and $C:$
    $AB+\overline{A}C=1$
    $AC+B=0$

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1 Answer

Best answer
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  1.  
    1. $A\ast A = AA+A'A' = A + A' = 1$
    2. $C\ast A= (A\ast B)\ast A = (AB + A'B')\ast A= (AB + A'B')A +(AB + A'B')'A'$
      $\qquad =(AB + A'B')A+(A'B+AB')A' = AB +0 +A'B+0 = B.$

 

  1. $AB + A'C= 1, AC + B = 0$

$\implies AC + B = 0,$ means both $B = 0$  and $AC = 0$

$\implies AB+ A'C = 1$

$\implies A'C = 1 \qquad \left[\because B = 0, AB = 0 \right]$

So, $C = 1$ and $A = 0$

$A = 0 , B = 0$ and $C = 1$

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