How to derive XOR from only NOR gates
AB' + A'B
= (0 + AB') + (A'B + 0)
= (AA' + AB') + (A'B + BB')
= A(A' + B') + B(A' + B')
= (A' + B')(A + B)
= (AB)'(A'B')'
= [(AB) + (A'B')]'
= [(A' + B')' + A'B']'
= [(A'A' + B'B')' + A'B']'
= ([(A + A)' + (B + B)']' + A'B')'
= ([(A + A)' + (B + B)']' + (A + B)')'
Commutative: [COM] p ∧ q ≡ q ∧ p p ∨ q ≡ q ∨ p
Associative: [ASS] (p ∧ q) ∧ r ≡ p ∧ (q ∧ r) (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
Distributive: [DIST] p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r) p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
Identity: p ∧ T ≡ p p ∨ F ≡ p
Negation: [NEG] p ∨ (∼p) ≡ T p ∧ (∼p) ≡ F
Double Negation: [DNEG] ∼(∼p) ≡ p
Idempotent: [ID] p ∧ p ≡ p p ∨ p ≡ p
Universal bound: [UB] p ∨ T ≡ T p ∧ F ≡ F
De Morgan’s: [DM] ∼(p ∧ q) ≡ (∼p) ∨ (∼q) ∼(p ∨ q) ≡ (∼p) ∧ (∼q)
Absorption: [ABS] p ∨ (p ∧ q) ≡ p p ∧ (p ∨ q) ≡ p
Negations of T and F: [NTF] ∼T ≡ F ∼F ≡ T
