## Wednesday, October 5, 2011

### EQ 13 Disjunction

(1) Axiom Symmetry of $$\vee$$: p $$\vee$$ q $$\hspace{0.2 cm} \equiv \hspace{0.2 cm}$$ q $$\vee$$ p

(2) Axiom Associativity of $$\vee$$: p $$\vee$$ (q $$\vee$$ r) $$\hspace{0.2 cm} \equiv \hspace{0.2 cm}$$ (p $$\vee$$ q ) $$\vee$$ r

(3) Axiom Idempotency of $$\vee$$: p $$\vee$$ p $$\hspace{0.2 cm} \equiv \hspace{0.2 cm}$$ p

(4) Axiom Distributivity of $$\frac{\vee}{\equiv}$$: p $$\vee$$ ( q $$\equiv$$ r) $$\hspace{0.2 cm} \equiv \hspace{0.2 cm}$$ (p $$\vee$$ q) $$\equiv$$ (p $$\vee$$ r)

(5) Axiom Excluded Middle p $$\vee$$ $$\neg$$p

(6) Theorem Zero of $$\vee$$: p $$\vee$$ true $$\hspace{0.2 cm} \equiv \hspace{0.2 cm}$$ true

(7) Theorem Identity of $$\vee$$ p $$\vee$$ false $$\hspace{0.2 cm} \equiv \hspace{0.2 cm}$$ p

(8) Theorem Distributivity of $$\frac{\vee}{\vee}$$: p $$\vee$$ ( q $$\vee$$ r) $$\hspace{0.2 cm} \equiv \hspace{0.2 cm}$$ (p $$\vee$$ q) $$\vee$$ (p $$\vee$$ r)

(9) Theorem p $$\vee$$ q $$\hspace{0.2 cm} \equiv \hspace{0.2 cm}$$ p $$\vee$$ $$\neg$$q $$\equiv$$ p