Exercise · ZW-ORDER-OF-QUANTIFIERS-001 · ★☆☆ Basic
In general, changing the order of ∀ and ∃...
Choose one option.
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- B. Can change the meaning
Explanation
Swapping \(\forall\) and \(\exists\) changes what is claimed about the elements, so the meaning can vary. That is why the order must be read carefully.
Review the concept: Order of quantifiers
For a predicate \(P(x,y)\), the order of the quantifiers can change the truth value of a formula.
\[\begin{gathered}\forall x\,\exists y\,P(x,y)\\\not\equiv\exists y\,\forall x\,P(x,y)\end{gathered}\]
More practice problems: order of quantifiers
- ZW-ORDER-OF-QUANTIFIERS-002 ∀x ∃y P(x,y) allows...
- ZW-ORDER-OF-QUANTIFIERS-003 ∃y ∀x P(x,y) states that...
- ZW-ORDER-OF-QUANTIFIERS-004 Which pair is not equivalent in general?
- ZW-ORDER-OF-QUANTIFIERS-005 The order of quantifiers matters especially when...
- ZW-ORDER-OF-QUANTIFIERS-006 In general, ∀x∃y R(x,y) and ∃y∀x R(x,y)...
- ZW-ORDER-OF-QUANTIFIERS-007 ∀x∃y R(x,y) allows...
- ZW-ORDER-OF-QUANTIFIERS-008 ∃y∀x R(x,y) states that...
- ZW-ORDER-OF-QUANTIFIERS-009 Select true statements about order.