Reflexive Axiom
\[a = a\]
\[a = a\]
Symmetric Axiom
\[a = b{\text{ then }}b = a\]
\[a = b{\text{ then }}b = a\]
Transitive Axiom
\[a = b{\text{ and }}b = c{\text{ then a}} = c\]
\[a = b{\text{ and }}b = c{\text{ then a}} = c\]
Additive Axiom
\[a = b{\text{ and }}c = d{\text{ then }}a + c = b + d\]
\[a = b{\text{ and }}c = d{\text{ then }}a + c = b + d\]
Multiplicative Axiom
\[a = b{\text{ and }}c = d{\text{ then }}ac = bd\]
\[a = b{\text{ and }}c = d{\text{ then }}ac = bd\]