13397061
Description
Mind Map by Luke Byrne, updated more than 1 year ago
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Created by Luke Byrne
almost 6 years ago
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Predicate Logic and Quantifiers
- "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)"
- QUANTIFIERS
- ∃ (existential quantifier)
- ∃xP(x) is true if P(x) is true for some value of x
- ∃xP(x) is true if P(x) is true for some value of x
- ∀ (universal quantifier)
- ∀xP(x) is true if P(x) is true for all allowable values of x
- ∀xP(x) is true if P(x) is true for all allowable values of x
- ∃! (for one and only one)
- ∃!xP(x) is true if P(x) is true for exactly one value and false for all other values of x
- ∃!xP(x) is true if P(x) is true for exactly one value and false for all other values of x
- ∃ (existential quantifier)
- ALTERNATION OF QUANTIFIERS
- ∀x∃y∀z P(x, y, z)
- N.B.: the order CANNOT be changed as it might modify the truth value of the statement
- N.B.: the order CANNOT be changed as it might modify the truth value of the statement
- ∀x∃y∀z P(x, y, z)
- NEGATION OF QUANTIFIERS
- ¬(∃xP(x)) ↔ ∀x¬P(x)
- ¬(∀xP(x)) ↔ ∃x¬P(x)
- ¬(∃xP(x)) ↔ ∀x¬P(x)
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