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Axioms & property
Math defintions for axioms and properties
Question | Answer |
---|---|
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 |