α → β // α ⊨ β // α ≤ β
⊨ ((P → Q) → P) → P - make a truth table
counterfactual conditionals:
if Oswald didn’t kill Kennedy,
then someone else would have
sufficient condition -
necessary condition - only if
Q if P - Q → P
Q only if P - P → Q
P if and only if Q
P ↔ Q ≈ (Q → P) ∧ (P → Q) - make a truth table
exercises:
- ¬S ∧ P
- P ∧ R
- ¬¬P
- P ∧ ¬R
- ¬P ∧ ¬S
- P ∨ Q
- (P ∨ Q) ∧ ¬(P ∧ Q)
- ¬S ∨ (P ∧ R)