Official PYQ · 1997Q2-1Boolean AlgebraMCQ1 mark

GATE CS 1997 Q2-1 — Boolean Algebra

Let $*$ be defined as $x * y = \bar{x} + y$ . Let $z = x * y$ . Value of $z * x$ is

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Answer: B

Given the binary operator $*$ defined as:

x * y = \bar{x} + y

We are given that $z = x * y = \bar{x} + y$ . We need to find the value of $z * x$ .

Applying the definition of the $*$ operator to $z * x$ :

z * x = \bar{z} + x

First, let's find the complement of $z$ using De Morgan's laws:

\bar{z} = \overline{\bar{x} + y} = \overline{\bar{x}} \cdot \bar{y} = x\bar{y}

Now, substitute $\bar{z}$ back into the expression for $z * x$ :

z * x = (x\bar{y}) + x

Using the absorption law of Boolean algebra ( $A + AB = A$ ):

x\bar{y} + x = x(1 + \bar{y}) = x \cdot 1 = x

Thus, $z * x = x$ , which corresponds to option B.

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Published 10 Oct 2026

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