The Rules of Inference

Question 1

Modus Ponens (Rule of Detachment)

Answer 1

p
p -> q
________
:. q

Question 2

Modus Tollens

Answer 2

~q
p -> q
________
:. ~p

Question 3

Laws of Syllogism (Hypothetical Syllogism)

Answer 3

p -> q
q -> r
________
:. p -> r

Question 4

Disjunctive Syllogism

Answer 4

p v q
~p
________
:. q

Question 5

Disjunctive Application (Addition Rule)

Answer 5

p
________
:. p v q

Question 6

Conjunctive Simplification

Answer 6

p ^ q
________
:. p

Question 7

Rule of Conjunction

Answer 7

p
q
________
:. p ^ q

Question 8

Resolution

Answer 8

p v q
~p v r
_________
:. q v r