Review of the 8 Basic Sentential Rules of Inference

Logical System
hausman

10/12/26

Modus Ponens (MP)

p⊃q,
p
∴ 
q

Modus Tollens (MT)

p⊃q,
~q
∴ 
~p

Disjunctive Syllogism(DS)

p∨q,
~p
∴ 
q

or, if desired,

p∨q,
~q
∴ 
p

Simplication (Simp)

p.q 
∴ 
p

or, if desired,

p.q 
∴ 
q

Conjunction (Conj)

p,
q 
∴ 
p.q

Hypothetical Syllogism (HS)

p⊃q,
q⊃r
∴ 
p⊃r

Addition(Add)

p
∴ 
p∨q

Constructive Dilemma (CD)

(p⊃q),
(r⊃s),
p∨r
∴ 
q∨s