Chapter 17
a, not a → b - principle of explosion
falsum - (upside down T) spits 0s
verum - T - spits 1s
inconsistency (between multiple propositions) - if A1…An entails falsum
contradiction (one proposition)
Chapter 18
if then
The Material Conditional - P → Q
P - antecedent
Q - consequent
→ is a binary propositional connective
| α | β | α → β |
|---|---|---|
| 1 | 1 | 1 |
| 1 | 0 | 0 |
| 0 | 1 | 1 |
| 0 | 0 | 1 |
| α → β ≈ ¬ α ∨ β | ||
| ¬ α → β ≈ α ∨ β | ||
| ¬ α ≈ α → ⊥ | ||
| contraposition - α → β ≈ ¬ β → ¬ α - both these propositions entail each other | ||
| modus ponens α → β, α ⊨ β | ||
| modus tollens α → β , ¬ β ⊨¬ α |
**slide 11 has all rules**