Summary: Rules of Inference of PL
| (p ⊃ q) | modus ponens
(mp) |
| p | |
| q |
| (p & q) | (p & q) | simplification
(simp) |
|
| p | q |
|
p |
conjoining
(conj) |
| q | |
| (p & q) |
| p | q | disjoining (disj) |
|
| (p v q) | (p v q) |
| (p v q) | (p v q) | disjunctive syllogism
(ds) |
|
| ~p | ~q | ||
| q | p |
| (p ⊃ q) | modus tollens
(mt) |
| ~q | |
| ~p |
|
(p ⊃ q) |
Hypothetical Syllogism
(hs) |
| (q ⊃ r) | |
| (p ⊃ r) |
| (p ⊃ q) | Dilemma
(dil) |
| (r ⊃ s) | |
| (p v r) | |
| (q v s) |
 |
 |