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# Axiom and Property

### Axioms and Properties

Question | Answer |
---|---|

Additive inverse | -x + x=0 |

Subtraction | x-y=x+(-y) |

Division | x divided by y = x •1/y |

Distributive Axiom | x(y+z) = xy+yz |

Commutative Axiom of Addition | x+y = y+x |

Commutative Axiom of Multiplication | xy=yx |

Associative Axiom of Addition | (x+y)+z=x+(y+z) |

Associative Axiom of Multiplication | (xy)z=x(yz) |

Additive Identity Axiom | x+0=x |

Multiplicative Identity Axiom | x • 1 = x |

Multiplicative Inverse Axiom | x • 1/x = 1 |

Multiplication Property of -1 | -1 • x= -x |

Multiplication Property of Zero | 0 • x= 0 |

Addition Property of Equality | x=y then x+z = y+z |

Multiplication Property of Equality | If x=y then xz=yz |

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 |

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