# Logic and Proof

### Exercises

#### Exercise 8

What is the reason for statement 15?

Given: *A* = *B*, *B* = *C*, *X* = *Y*, *Y* = *Z*, *H* = *G*, *G* ≠ 0

Prove:

Statements | Reasons |

1. A = B | Given |

2. B = C | Given |

3. X = Y | Given |

4. Y = Z | Given |

5. H = G | Given |

6. G ≠ 0 | Given |

7. A = C | Transitive Property (1 and 2) |

8. H ≠ 0 | Substitution Property (5 and 6) |

9. AB = BB | Multiplication Property (1) |

10. AB = BC | Substitution Property (9 and 2) |

11. | Division Property (10 and 6) |

12. | Substitution Property (11 and 5) |

13. | Multiplication Property (12) |

14. X = Z | Transitive Property (3 and 4) |

15. | ? |

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