| A | B |
|---|
| Commutative Axiom for Addition | x+y=y+x |
| Commutative Axiom for Multiplication | xy=yx |
| Associative Axiom for Addition | (x+y)+z=x+(y+z) |
| Associative Axiom for Multiplication | (xy)z=x(yz) |
| Additive Identity Axiom | x+0=x |
| Multiplicative Identity Axiom | 1(x)=x |
| Additive Inverse Axiom | x+(-x)=0 |
| Multiplicative Inverse Axiom | x(1/x)=1 |
| Addition Property of Equality | x+(z)=y+(z) |
| Multiplication Property of Equality | x(z)=y(z) |
| Subtraction Property of Equality | x-(z)=y-(z) |
| Division Property of Equality | x/(z)=y/(z) |
| Transitive Axiom of Equality | If x=y, and y=z, then x=z |
| Symmetric Axiom of Equality | If x=y, then y=x |
| Reflexive Axiom of Equality | x=x |
| Distributive Axiom | x(y+z)=xy+xz |
