## Wednesday, October 5, 2011

### EQ 15 Equivalence and True

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

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

(3) Axiom: Identity of $$\equiv$$: true $$\equiv$$ q $$\equiv$$ q

(4) Theorem: true

(5) Reflexivity of $$\equiv$$: p $$\equiv$$ p