Inference Rules

Question 1

Generalisation

Answer 1

p
∴ p V q

q
∴ p V q

Question 2

Specialisation

Answer 2

p Λ q
∴ p

p Λ q
∴ q

Question 3

Conjunction

Answer 3

p
q
∴ p Λ q

Question 4

Modus ponens

Answer 4

p -> q
p
∴ q

Question 5

Modus tollens

Answer 5

p -> q
~q
∴ ~p

Question 6

Transitivity

Answer 6

p -> q
q -> r
∴ p -> r

Question 7

Elimination

Answer 7

p V q
~p
∴ q

p V q
~q
∴p

Question 8

Proof by division into cases

Answer 8

p V q
p -> r
q -> r
∴ r

Question 9

Contradiction rule

Answer 9

~p -> c

∴ p