GATE CSE 1988 | Question: 2-iii

Question

Let $*$ be defined as a Boolean operation given as $x*y = \overline{x}\;\;\overline{y}+xy$ and let $C=A*B$. If $C=1$ then prove that $A=B$.

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Answer 1

$C=A\ast B$

$\implies C=\overline{A}\;\;\overline{B}+AB$

$\implies C = \overline{A\text{ XOR }B}$

$\implies C = A\text{ XNOR }B$

Truth table is: $${\begin{array}{ccc}\hline
\textbf{A}&    \textbf{B}&  \textbf{C} \\\hline
0& 0 & 1  \\
0&     1& 0\\  
1&     0&  0     \\
1&1&1  
\end{array}}$$ When $C = 1 $, observing the truth table we can say $ A=B.$

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Great explanations

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