Exercise · ZW-ORDER-OF-QUANTIFIERS-009 · ★★★ Advanced
Select true statements about order.
Choose one option.
Show answer
- B. Changing quantifiers can change the meaning
Explanation
Changing the order of quantifiers can alter the truth value, as \(\forall x\,\exists y\) versus \(\exists y\,\forall x\) shows. The other statements are false: order does matter, and a global witness is stronger.
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-001 In general, changing the order of ∀ and ∃...
- 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...