How does modus tollens relate to contrapositives in logic?
A contrapositive negates and reverses a conditional (if–then) statement. For example, the contrapositive for the statement “If P, then Q” is “If not Q, then not P.”
Modus tollens validates the contrapositive, demonstrating that “not P” follows logically from “not Q” as follows:
- If P, then Q.
- Not Q.
- Therefore, not P.