Known proposition formula (¬ p → q) → (¬ q ∨ p) (\lnot p\rightarrow q)\rightarrow(\lnot q \lor p)(¬p→q)→(¬q∨p)
Construct truth table
| p, | ( ¬ p → q ) (\lnot p\rightarrow q) (¬p→q) | ( ¬ q ∨ p ) (\lnot q \lor p) (¬q∨p) | ( ¬ p → q ) → ( ¬ q ∨ p ) (\lnot p\rightarrow q)\rightarrow(\lnot q \lor p) (¬p→q)→(¬q∨p) |
|---|---|---|---|
| 0 ,0 | 0 | 1 | 1 |
| 0,1 | 1 | 0 | 0 |
| 1,0 | 1 | 1 | 1 |
| 1,1 | 1 | 1 | 1 |
Disjunctive paradigm
( ¬ p → q ) → ( ¬ q ∨ p ) (\lnot p\rightarrow q)\rightarrow(\lnot q \lor p) (¬p→q)→(¬q∨p)
( p ∨ q ) → ( ¬ p ∨ q ) (p\lor q)\rightarrow(\lnot p \lor q) (p∨q)→(¬p∨q)
¬ ( p ∨ q ) ∨ ( ¬ p ∨ q ) \lnot(p\lor q)\lor(\lnot p \lor q) ¬(p∨q)∨(¬p∨q)
( ¬ p ∧ ¬ q ) ∨ ( ¬ q ∨ p ) (\lnot p \land \lnot q)\lor (\lnot q \lor p) (¬p∧¬q)∨(¬q∨p)
( ¬ p ∧ ¬ q ) ∨ ¬ q ∨ p (\lnot p\land \lnot q)\lor \lnot q\lor p (¬p∧¬q)∨¬q∨p
( ¬ p ∧ ¬ q ) ∨ ¬ q ∧ ( p ∨ ¬ p ) ∨ p ∧ ( q ∨ ¬ q ) (\lnot p\land \lnot q)\lor \lnot q\land(p\lor \lnot p)\lor p\land(q\lor \lnot q) (¬p∧¬q)∨¬q∧(p∨¬p)∨p∧(q∨¬q)
( ¬ p ∧ ¬ q ) ∨ ( ¬ q ∧ p ) ∨ ( ¬ q ∧ ¬ p ) ∨ ( p ∧ q ) ∨ ( p ∧ ¬ q ) (\lnot p\land \lnot q)\lor(\lnot q\land p)\lor (\lnot q\land \lnot p)\lor (p\land q)\lor(p\land \lnot q) (¬p∧¬q)∨(¬q∧p)∨(¬q∧¬p)∨(p∧q)∨(p∧¬q)
( ¬ p ∧ ¬ q ) ∨ ( ¬ q ∧ p ) ∨ ( p ∧ q ) (\lnot p\land \lnot q)\lor (\lnot q\land p)\lor(p\land q) (¬p∧¬q)∨(¬q∧p)∨(p∧q)