p → q is logically equivalent to ________ ans. ¬p ∨ q ¬p ∨ ¬q p ∨ ¬q ¬p ∧ q

The logical equivalence of "p → q" is "¬p ∨ q". This is based on the definition of implication in logic. Here's the step by step explanation:

1. "p → q" is an implication. It means "if p then q".

2. The only way for an implication to be false is if the first part (p) is true and the second part (q) is false.

3. Therefore, the implication is true in all other cases: if p is false, or if q is true.

4. This is exactly what "¬p ∨ q" says: either p is not true (¬p), or q is true.

The other options are not logically equivalent to "p → q".

• "¬p ∨ ¬q" would mean "either p is not true, or q is not true", which is not the same as "if p then q".
• "p ∨ ¬q" would mean "either p is true, or q is not true", which is also not the same as "if p then q".
• "¬p ∧ q" would mean "p is not true and q is true", which is again not the same as "if p then q".