Given: p is true Prove: 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. What type of proof is illustrated above? A. proof by contradiction B. proof by contraposition C. proof by law of detachment D. proof by law of syllogism

Question

Laci Holmes

Mathematics

19 January, 03:21

Given: p is true Prove: 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. What type of proof is illustrated above? A. proof by contradiction B. proof by contraposition C. proof by law of detachment D. proof by law of syllogism

+1

Answers (1)

Know the Answer?

Beau Garrison · Answer 1

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.