Question

The dual of \( x \lor (y \land 0) \) is

• A. \( x \land (y \lor 1) \)
• B. \( x \lor (y \lor 1) \)
• C. \( x' \lor (y \land 0) \)
• D. \( (x \lor y) \land 0 \)

Hint:

The duality principle is a powerful tool in Boolean algebra. If a Boolean expression is true, its dual is also true.

Answer 1

The Correct Option is A

To find the dual of a Boolean expression, we apply the following transformations:
\begin{itemize} \item Replace \( \lor \) with \( \land \)
\item Replace \( \land \) with \( \lor \)
\item Replace \( 0 \) with \( 1 \)
\item Replace \( 1 \) with \( 0 \)
\item Leave the variables unchanged
\end{itemize} Given expression: \( x \lor (y \land 0) \)
Applying the duality principle:
\( x \) remains \( x \)
\( \lor \) becomes \( \land \)
\( ( \) remains \( ( \)
\( y \) remains \( y \)
\( \land \) becomes \( \lor \)
\( 0 \) becomes \( 1 \)
\( ) \) remains \( ) \)
\ So, the dual of \( x \lor (y \land 0) \) is \( x \land (y \lor 1) \).