Exercise · ZW-NEGATION-OF-QUANTIFIERS-003 · ★☆☆ Basic
"Not all students passed" is equivalent to...
Choose one option.
Show answer
- C. At least one student did not pass
Explanation
'Not all passed' negates 'all passed', so it is equivalent to 'at least one did not pass'.
Review the concept: Negation of quantifiers
For a predicate \(P(x)\) over \(D\), negating a quantifier swaps the quantifier and negates the predicate.
\[\begin{gathered}\neg\forall x P(x)\equiv\exists x\neg P(x)\\\neg\exists x P(x)\equiv\forall x\neg P(x)\end{gathered}\]
More practice problems: negation of quantifiers
- ZW-NEGATION-OF-QUANTIFIERS-001 The negation of ∀ x P(x) is...
- ZW-NEGATION-OF-QUANTIFIERS-002 The negation of ∃ x P(x) is...
- ZW-NEGATION-OF-QUANTIFIERS-004 What operation appears when negating a quantifier?
- ZW-NEGATION-OF-QUANTIFIERS-005 Which equivalence is correct?
- ZW-NEGATION-OF-QUANTIFIERS-006 The negation of ∀ x P(x) is equivalent to...
- ZW-NEGATION-OF-QUANTIFIERS-007 The negation of ∃ x P(x) is equivalent to...
- ZW-NEGATION-OF-QUANTIFIERS-008 To negate 'every number is positive' it is enough to state...
- ZW-NEGATION-OF-QUANTIFIERS-009 Select the correct equivalence.
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