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ZWMath›Logic›Predicate logic›Existential quantifier›ZW-EXISTENTIAL-QUANTIFIER-001
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AreaLogicTopicPredicate logic
Propositional logic11
  • Proposition
  • Logical operator
  • Negation
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Predicate logic5
  • Predicate
  • Universal quantifier
  • Existential quantifier
  • Negation of quantifiers
  • Order of quantifiers
Proof theory6
  • Axiomatic system
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Completeness and incompleteness2
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Exercise · ZW-EXISTENTIAL-QUANTIFIER-001 · ★☆☆ Basic

The symbol of the existential quantifier is...

Choose one option.

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  • B. ∃

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Explanation

The existential quantifier symbol is \(\exists\), read as 'there exists'. The other symbols are the universal quantifier, negation and disjunction.

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Review the concept: Existential quantifier

Given a predicate \(P(x)\) over a domain \(D\), the existential quantifier asserts that \(P(x)\) is true for some \(x\in D\).

\[\exists x\,P(x)\]

More practice problems: existential quantifier

  • ZW-EXISTENTIAL-QUANTIFIER-002 ∃x P(x) means that P(x) holds...
  • ZW-EXISTENTIAL-QUANTIFIER-003 To prove an existential statement it is enough to provide...
  • ZW-EXISTENTIAL-QUANTIFIER-004 Which statement is existential?
  • ZW-EXISTENTIAL-QUANTIFIER-005 If there is at least one x in the domain with P(x) true, ∃x P(x) is...
  • ZW-EXISTENTIAL-QUANTIFIER-006 The symbol ∃ is read...
  • ZW-EXISTENTIAL-QUANTIFIER-007 ∃x P(x) is true when...
  • ZW-EXISTENTIAL-QUANTIFIER-008 To prove ∃x P(x), it is usually enough to exhibit...
  • ZW-EXISTENTIAL-QUANTIFIER-009 Select expressions that imply there is at least one object.

ZW-EXISTENTIAL-QUANTIFIER-002 →

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