Which option is the inverse of P -> Q?

Which option is the inverse of P -> Q?

• A. Not P -> Not Q
• B. Q -> P
• C. Not Q -> Not P
• D. P -> Q

Answer: (A)

When you see a conditional like “If P then Q,” the inverse is formed by negating both parts while keeping the implication the same: “If not P, then not Q.” That’s why the statement not P -> not Q is the inverse. It follows the rule of negating both the antecedent and the consequent without changing the direction of the implication. It helps to distinguish the related forms: the converse swaps P and Q (Q -> P), and the contrapositive both negates and reverses (not Q -> not P), which is actually logically equivalent to the original. The original stays P -> Q. So the option that matches the inverse is the one stating not P -> not Q.

When you see a conditional like “If P then Q,” the inverse is formed by negating both parts while keeping the implication the same: “If not P, then not Q.” That’s why the statement not P -> not Q is the inverse. It follows the rule of negating both the antecedent and the consequent without changing the direction of the implication.

It helps to distinguish the related forms: the converse swaps P and Q (Q -> P), and the contrapositive both negates and reverses (not Q -> not P), which is actually logically equivalent to the original. The original stays P -> Q. So the option that matches the inverse is the one stating not P -> not Q.