Given the following proof:
p
→ q is true Assume ~q is true. Then ~q → r, and r → s. Since s → ~p, ~q
→ ~p by the law of syllogism. Therefore, p → q is true.
We can see that the conclusion was drawn from the fact that since ~q
→ ~p, then p → q.
This is known as contraposition.
Contraposition in logic is the conversion of a proposition from, for example: all A is B to all not-B is not-A.
