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# Axioms & property

### Math defintions for axioms and properties

commutative axiom for addition x + y = y + x
commutative axion for multiplication xy= yx
Associative axiom for addition (x + y) + z = x + (y + z)
Associative axion for multiplication (xy)z = x(yz)
Distributive axiom for multiplication over addition x (y + z) = xy +xz
Additive Identity Axiom x + 0 = x
Additive Inverses Axiom x + (-x) = 0
Multiplicative Identity Axiom x ' 1 = x
Multiplicative Inverses Axiom x ' 1/x = 1
Multiplication property of -1 -1 ' x = -x
Multiplication property of 0 0 ' x = 0
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
Addition property of equality if x = y, then x + z = y + z
Multiplication property of equality If x = y, then xz = yz
Created by: pragu :)