Rule of Inference

Question 1

p
p -> q
∴ q

Answer 1

Modus Ponens

Question 2

¬q
p -> q
∴ ¬q

Answer 2

Modus Tollens

Question 3

p -> q
q -> r
∴ p -> r

Answer 3

Hypothetical Syllogism

Question 4

p v q
¬p
∴ q

Answer 4

Disjunctive Syllogism

Question 5

p

∴ p v q

Answer 5

Addition

Question 6

p ^ q

∴ p

Answer 6

Simplification

Question 7

p
q
∴ p ^ q

Answer 7

Conjunation

Question 8

p v q
¬p v r
∴ q v r

Answer 8

Resolution

Question 9

∀x P(x)

∴ P(c)

Answer 9

Universal conditionnal statment

Question 10

P(c) for an arbitrary c

∴ ∀x P(x)

Answer 10

Universal Generalization

Question 11

∃x P(x)

∴ P(c) for some element c

Answer 11

Existential conditional

Question 12

p(c) for some c

∴ ∃x P(x)

Answer 12

Existential generalization

Question 13

∀x (P(x) -> Q(x))
P(a), where a ∈ the domain
∴ Q(a)

Answer 13

universal modus ponens

Question 14

∀x (P(x) -> Q(x))
¬Q(a), where a ∈ the domain
∴ ¬P(a)

Answer 14

universal Modus Tollens