Question

Switching current of \( (p \land q) \lor (p \land (q \lor p \lor r)) \)?

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

Hint:

For simplifying Boolean expressions, apply distributive, associative, and absorption laws. Look for opportunities to simplify terms that appear more than once.

Answer 1

The Correct Option is C

The given Boolean expression is: \[ (p \land q) \lor (p \land (q \lor p \lor r)). \] First, simplify the second part of the expression, \( p \land (q \lor p \lor r) \). By the distributive property: \[ p \land (q \lor p \lor r) = (p \land q) \lor (p \land p) \lor (p \land r). \] Since \( p \land p = p \), we can simplify this further: \[ = (p \land q) \lor p \lor (p \land r). \] Now, the original expression becomes: \[ (p \land q) \lor (p \land q) \lor p \lor (p \land r). \] Simplify this expression by combining like terms: \[ = p \lor (p \land q) \lor (p \land r). \] Finally, by the absorption law, \( p \lor (p \land q) = p \), so the expression reduces to: \[ p \lor (p \land r). \] Thus, the final simplified expression is: \[ p \land \sim q \lor p \lor r. \] Thus, the correct answer is \( p \land \sim q \lor p \lor r \).