Question

The proposition $ \neg P \cup Q $ is equivalent to which of the following?

• A. \( P \cap \neg Q \)
• B. \( P \rightarrow Q \)
• C. \( Q \rightarrow P \)
• D. \( Q \cap P \)

Hint:

The disjunction \( \neg P \cup Q \) is logically equivalent to the implication \( P \rightarrow Q \).

Answer 1

The Correct Option is B

The logical expression \( \neg P \cup Q \) can be interpreted as "either \( P \) is false or \( Q \) is true". This is a logical disjunction. The logical equivalence of \( \neg P \cup Q \) is the implication \( P \rightarrow Q \), which can be rewritten as "if \( P \) is true, then \( Q \) must be true".
Thus, the correct equivalent proposition is \( P \rightarrow Q \).