Rules Of Inference & Replacement

Question 0

What is the role of inference for Simplification (Simp)?

Answer 0

p & q

p

Question 1

What is the rule of inference for Conjunction (Conj)?

Answer 1

p
q
p & q

Question 2

What is the rule of inference for Addition (add)?

Answer 2

p

p v q

Question 3

What is the rule of inference for Disjunctive Syllogism (DS)?

Answer 3

p v q
~p
q

Question 4

What is the rule of inference for Excluded Middle Introduction (E-MI)?

Answer 4

p v ~p

Question 5

What is the rule of replacement for Commutation (Com)?

Answer 5

p & q :: q & p

p v q :: q v p

Question 6

What is the rule of replacement for Association (Assoc)?

Answer 6

p & (q & r) :: (p & q) & r
p v (q v r) :: (p v q) v r

Question 7

What is the rule of replacement for Distribution (Dist)?

Answer 7

p & (q v r) :: (p & q) v (p & r)
p v (q & r) :: (p v q) & (p v r)

Question 8

What is the rule of replacement for Double Negation (DN)?

Answer 8

p :: ~~p

Question 9

What is the rule of replacement for DeMorgan (De M)

Answer 9

~p & ~q :: ~(p v q)

~p v ~q :: ~(p & q)

Question 10

What is the rule of inference for Modus Ponens (MP)?

Answer 10

p ⊃ q
p
q

Question 11

What is the rule of inference for Modus Tollens (MT)?

Answer 11

p ⊃ q
~q
~p

Question 12

What is the rule of inference for hypothetical syllogism (HS)?

Answer 12

p ⊃ q
q ⊃ r
p ⊃ r

Question 13

What is the rule of inference for Constructive Dilemma (CD)?

Answer 13

p v q
p ⊃ r
q ⊃ s
r v s

Question 14

What is the rule of replacement for Transposition (Trans)?

Answer 14

p ⊃ q :: ~q ⊃ ~p

Question 15

What is the rule of replacement for Exportation (Exp)?

Answer 15

(p & q) ⊃ r :: p ⊃ (q ⊃ r)

Question 16

What is the rule of replacement for Implication (Impl)?

Answer 16

p ⊃ q :: ~p v q

Question 17

What is the rule of replacement for Equivalence (Equiv)?

Answer 17

p ≡ q :: (p ⊃ q) & (q ⊃ p)

p ≡ q :: (p & q) v (~p & ~q)