Question

The Boolean expression: \[ \neg (p \vee q) \vee (\neg p \wedge q) \] is equivalent to:

• A. \( p \)
• B. \( q \)
• C. \( \neg q \)
• D. \( \neg p \)

Hint:

Using De Morgan's law and distribution simplifies complex Boolean expressions.

Answer 1

The Correct Option is D

Applying De Morgan's Law, we get: \[ eg (p \vee q) = eg p \wedge eg q \] Therefore: \[ (eg p \wedge eg q) \vee (eg p \wedge q) \] Using the distributive law: \[ eg p \wedge (eg q \vee q) \] Since \( eg q \vee q = 1 \) (a tautology): \[ eg p \wedge 1 = eg p \] The Boolean expression simplifies to: \[ eg p \]