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propositions

Proposition 4.2. For statements p,q,rp, q, r, (1) p ∧ q ⇔ q ∧ p (2) p ∨ q ⇔ q ∨ p (3) p ∧ (q ∧ r) ⇔ (p ∧ q) ∧ r (4) p ∨ (q ∨ r) ⇔ (p ∨ q) ∨ r (5) p ∧ (q ∨ r) ⇔ (p ∧ q) ∨ (p ∧ r) (6) p ∨ (q ∧ r) ⇔ (p ∨ q) ∧ (p ∨ r) (7) p ∧ p ⇔ p (8) p ∨ p ⇔ p (9) ¬(¬p) ⇔ p (10) ¬(p ∧ q) ⇔ ¬p ∨ ¬q (11) ¬(p ∨ q) ⇔ ¬p ∧ ¬q

Proposition 4.3. For arbitrary sets A,B,CA, B, C of a universal set UU, (1) A ∩ B = B ∩ A (2) A ∪ B = B ∪ A (3) A ∩ (B ∩ C) = (A ∩ B) ∩ C (4) A ∪ (B ∪ C) = (A ∪ B) ∪ C (5) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (6) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (7) A ∩ A = A (8) A ∪ A = A ![[chrome_6NUKDHbgG3.png]] (Line on top of set = complement of the set)