Predicate Logic and Quantifiers

Descrição

Senior Freshman Mathematics Mapa Mental sobre Predicate Logic and Quantifiers, criado por Luke Byrne em 22-04-2018.
Luke Byrne
Mapa Mental por Luke Byrne, atualizado more than 1 year ago
Luke Byrne
Criado por Luke Byrne aproximadamente 6 anos atrás
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Resumo de Recurso

Predicate Logic and Quantifiers
  1. "In predicate logic, propositions depend on variables x, y, z, so their truth value may change depending on which values these variables assume: P(x), Q(x, y), R(x, y, z)"
    1. QUANTIFIERS
      1. ∃ (existential quantifier)
        1. ∃xP(x) is true if P(x) is true for some value of x
        2. ∀ (universal quantifier)
          1. ∀xP(x) is true if P(x) is true for all allowable values of x
          2. ∃! (for one and only one)
            1. ∃!xP(x) is true if P(x) is true for exactly one value and false for all other values of x
          3. ALTERNATION OF QUANTIFIERS
            1. ∀x∃y∀z P(x, y, z)
              1. N.B.: the order CANNOT be changed as it might modify the truth value of the statement
            2. NEGATION OF QUANTIFIERS
              1. ¬(∃xP(x)) ↔ ∀x¬P(x)
                1. ¬(∀xP(x)) ↔ ∃x¬P(x)

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