Laws of Algebra of Statements

Laws of Algebra of Statements

(i) Idempotent Laws

(a) p ∨ p ≡ p

(b) p ∧ p ≡ p

(ii) Associative Laws

(a) (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

(b) (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

(iii) Commutative Laws

(a) p ∨ q ≡ q ∨ p

(b) p ∧ q ≡ q ∧ P

(iv) Distributive Laws

(a) p ∨ (q A r) ≡ (p ∨ q) ∧ (p ∨ r)

(b) p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

(v) De Morgan's Laws

(a) ~(p ∨ q) ≡ (~ p) ∧ (,_ q)

(b) ~(p ∧ q) ≡ (~ p) ∨ (~ q)

(vi) Identity Laws

(a) p ∧ F ≡ F

(b) p ∧ T ≡ p

(c) p ∨ T ≡ T

(d) p ∨ F ≡ p

(vii) Complement Laws

(a) p ∨ (~ p) ≡ T

(b) p ∧ (~ p) ≡ F

(c) ~ (~p) ≡ p

(d) ~ T ≡ F, ~ F ≡ T

Important Points to be Remembered

(i) The number of rows of table is depend on the number of statements.

(a) If p is false, then ~ p is true.

(b) If P is true, then ~ p is false.

(ii) (a) The converse of p => q is q => p.

(b) The inverse of p => q is ~ p => ~ q.

(iii) The contrapositive of p => q is ~ q => ~ p.

A statement which is neither a tautology nor a contradiction is a contingency.