Question

The compound proposition ~p or q is logically equivalent to:

• A. p implication q
• B. q implication p
• C. ~q implication p
• D. p and q

Answer 1

Answer: (A)

p implication q

Answer 2

The logical proposition ~p or q is a standard equivalence for p implication q (or p -> q). This can be verified using truth tables where both expressions yield identical truth values for all combinations of p and q.

Truth Table for ~p or q:

p	q	~p	~p or q
True	True	False	True
True	False	False	False
False	True	True	True
False	False	True	True

Truth Table for p -> q:

p	q	p -> q
True	True	True
True	False	False
False	True	True
False	False	True

Since the truth columns for ~p or q and p -> q are identical, they are logically equivalent.