Question

The Boolean expression \( (\sim(p \land q)) \lor q \) is equivalent to:

• A. \( q \to (p \land q) \)
• B. \( p \to q \)
• C. \( p \sim(p \to q) \)
• D. \( p \to (p \lor q) \)

Hint:

When simplifying Boolean expressions, utilize truth tables or logical equivalences to identify the simplest form that matches the options.

Answer 1

The Correct Option is D

The given logical expression is: \[ (\sim(p \land q)) \lor q. \] Step 1: Simplify the expression. Applying Boolean algebra, we have: \[ \sim(p \land q) = \sim p \lor \sim q. \] Thus, the expression becomes: \[ (\sim p \lor \sim q) \lor q = \sim p \lor q. \] Step 2: Rewrite in implication form. Recognizing that: \[ \sim p \lor q = p \to (p \lor q), \] we conclude that the simplified expression is equivalent to \( p \to (p \lor q) \). Therefore, the correct answer is \( \boxed{(4)} \).