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# Exam 2

### MAT 300 Mathematical Structures

Term | Definition |
---|---|

Existential Instantiation | Introducing a new variable x into the proof to stand for an object for which P(x) is true. This means that you can now assume that P(x) is true |

Universal Instantiation | You can plug in any value, say a, for x and use this given to conclude that P(a) is true. |

m divides n (m|n) | n is evenly divisible by m |

Odd integers | |

Even integers | |

Uniqueness (E!) | |

Ordered pairs | Pairs of values in which the order of the values makes a difference (a, b) |

First coordinate | The first value in an ordered pair, so a |

Second coordinate | The second value in an ordered pair, so b |

Cartesian product (AxB) of two sets | The set of all ordered airs in which the first coordinate is an element of A and the second is an element of B |

Relations from A to B | Suppose A and B are sets. Then a set R (is a subset of) AxB is called a relation from A to B |

Domain of relations and functions | p. 172 |

Range of relations and functions | p. 172 |

Inverse of relations | p. 172 |

Composition of relations and functions | |

Identity relation and function (iA) on a set A | |

Reflexive relations | p. 184-185 |

Symmetric relations | p. 184-185 |

Transitive relations | p. 184-185 |

Antisymmetric relations | p. 189 |

Partial orders | A relation R on a set A that is reflexive, transitive, and antisymmetric |

Total orders | p. 190 |

Smallest element | p. 189- |

Largest element | |

Equivalence relations | |

Equivalence classes | |

Partitions | |

A modulo R (A/R) | |

Congruence modulo | |

Functions f: A --> B | |

Codomain of a function |

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