Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Exam 1

### MAT 300 Mathematical Structures

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

Def: Tautology | Formulas that are always true ex) P or not P |

Def: Contradiction | Formulas that are always false ex) P and not P |

Def: Converse | The reversal of an if-then statement. Logically equivalent to inverse. ex) P -> Q ; Q -> P |

R | The set of all real numbers, containing all rational and irrational numbers. Q, N , Z are the subsets of the set R. |

Q | The set of all rational numbers. The rational numbers are any number which could be written like p/q, where p and q are integers. |

N | The set of all natural numbers like:1,2,3,4,5,....... The set has starting number 1 and the consecutive numbers increments by 1 . It has no end. |

Z | Integers (positive or negatives including zero). |

Def: Statement | An assertion (about mathematics) that is objectively either true or false |

Def: Argument | A sequence of statements. All except the last are premises, while the last is a conclusion. |

Def: Valid Argument | P1, P2, P3, ... , Pk | Q Q is true when all Ps are true (conclusion is true whenever all premises are true |

Def: Proof of an Assertion Q | A sequence of true statements connected with valid arguments and ending with Q |

Def: Equivalence | Two statements with the same truth table Symbol: <=> |

Def: Set | A collection of objects (elements) |

Free Variables | Truth value depends on variable |

Bound Variables | Variable can be replaced or eliminated |

DeMorgan's Law | ~(A or B) --> ~A and ~B ~(A and B) --> ~A or ~B |

Def: Contrapositive | Reversing if-then and adding "not" to both sides (combines inverse and converse). Logically equivalent to conditional! ex) P --> Q ; ~Q --> ~P |

Def: Inverse | Adds not to both sides. Logically equivalent to converse. |

Def: Power Set | The set whose elements are all subsets of A P(A) = { x | x is a subset of A } |

Commutative Laws | P ^ Q is equivalent to Q ^ P P or Q is equivalent to Q or P |

Associative Laws | When a statement has all "and"s or "or"s, it doesn't matter how you separate them P ^ (Q ^ R) is equivalent to (P ^ Q) ^ R P or (Q or R) is equivalent to (P or Q) or R |

Idempotent Laws | P and/or P is equivalent to P |

Distributive Laws | P ^ (Q or R) is equivalent to (P ^ Q) or (P ^ R) P or (Q ^ R) is equivalent to (P or Q) ^ (P or R) |

Absorption Laws | P or (P ^ Q) is equivalent to P P ^ (P or Q) is equivalent to P |

Modus Ponens | If you know that P is true and P --> Q is true, then Q is also true |

Modus Tollens | If you know that P --> Q is true and Q is false, then Q is false |

Proof by Contradiction | Show that if a proposition is false, a contradiction is implied |

Def: Elements | Objects in sets |

Created by:
arianaflores