# Logic Definitions

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xokihele's
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2017-06-15 15:27

## Section 1

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

Reflexivity | iff for all d in S the pair ⟨d, d⟩ is an element of R. |

Function | iff for all d, e, f: if ⟨d, e⟩ ∈ R and ⟨d, f ⟩ ∈ R then e = f . |

Equivalence Relation | iff R is reflexive on S, symmetric on S and transitive on S. |

Transitivity | iff for all d, e, f, if ⟨d, e⟩ ∈ R and ⟨e, f ⟩ ∈ R, then also ⟨d, f ⟩ ∈ R |

Set | a collection of objects, the elements of the set. |

Binary Relation | iff it contains only ordered pairs. |

Symmetry | iff for all d, e of S: if ⟨d, e⟩ ∈ R then ⟨e, d⟩ ∈ R. |

Asymmetry | iff for no elements d, e of S, if ⟨d, e⟩ ∈ R then ⟨e, d⟩ ∈ R. |

Antisymmetry | iff for no two distinct elements d, e of S: if ⟨d, e⟩ ∈ R then ⟨e, d⟩ ∈ R. |

## Section 2

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

Logical Validity | iff there is no interpretation under which the premisses are all true and the conclusion is false. |

Logical Entailment (Double Turnstile) | if the set of sentences on the left are true, the sentence on the right must be true |

Truth Functional | iff the truth-value of the compound sentence cannot be changed by replacing a direct subsentence with another having the same truth-value. |

Semantic Consistency | iff there is an L1 structure under which all sentences of Γ are true. |

Tautology (Logical Truth) | iff: φ is true under all L1 structures, true under any interpretation |

Contradiction | iff: φ is not true under any L1 structure, false under any interpretation. |

Logical Equivalence | iff: φ and ψ are true in exactly the same L1 structures. |

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