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