Question

The statement pattern \( \sim (p \vee q) \vee (\sim p \wedge q) \) is equivalent to

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

Hint:

When simplifying logical expressions, apply logical equivalences such as De Morgan's laws and distributive properties.

Answer 1

The Correct Option is D

Step 1: Simplify the statement pattern.
Using logical equivalences and simplifying the expression, we find that \( \sim (p \vee q) \vee (\sim p \wedge q) \) is equivalent to \( q \).
Step 2: Conclusion.
Thus, the equivalent statement is \( q \), corresponding to option (D).