Rules of Inference I

Question 1

Modus Ponens / Law of Direct Reasoning

Answer 1

((p -> q) ^ p) => q

Question 2

Modus Tollens / Law of Indirect Reasoning

Answer 2

((p -> q) ^ ~q) => ~p

Question 3

Hypothetical Syllogism / Law of Transitive Reasoning

Answer 3

(p -> q) ^ (q -> r) => (p -> r)

Question 4

Disjunctive Syllogism

Answer 4

(p v q) ^ ~p => q
(p v q) ^ ~q => p

Question 5

Law of Addition

Answer 5

p => (p v q)