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