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:

  1. ¬S ∧ P
  2. P ∧ R
  3. ¬¬P
  4. P ∧ ¬R
  5. ¬P ∧ ¬S
  6. P ∨ Q
  7. (P ∨ Q) ∧ ¬(P ∧ Q)
  8. ¬S ∨ (P ∧ R)