Solutions Quantifiers3 2: Difference between revisions
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(Created page with "1. For every person there is at least one person who loves him / her: ∀x (PERSON (x) → ∃y (PERSON (y) & LOVE (x, y)) 2. There is one person that is loved by everyone:...") |
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1. For every person there is at least one person who loves him / her: | 1. For every person there is at least one person who loves him / her: | ||
∀x (PERSON (x) | <!-- ∀x (PERSON (x) ⊃ ∃y (PERSON (y) & LOVE (x, y)) --> | ||
∀''x'' ('''person'''(''x'') ⊃ ∃''y'' ('''person'''(''y'') ∧ '''love'''(''x'',''y'') | |||
Or, in restricted-quantifier notation: | |||
∀''x'' ('''person'''(''x'') : ∃''y'' ('''person'''(''y'') : '''love'''(''x'',''y'') | |||
2. There is one person that is loved by everyone: | 2. There is one person that is loved by everyone: | ||
∃x (PERSON (x) → ∀y (PERSON (y) & LOVE (y, x)) | <!-- ∃x (PERSON (x) → ∀y (PERSON (y) & LOVE (y, x)) --> | ||
∃''y'' ('''person'''(''y'') ⊃ ∀''x'' ('''person'''(''x'') ∧ '''love'''(''x'',''y'') | |||
Or, in restricted-quantifier notation: | |||
∀''x'' ('''person'''(''x'') : ∃''y'' ('''person'''(''y'') : '''love'''(''x'',''y'') | |||
[[Exercise_Quantifiers#Scopal_Ambiguity|Return to Excercise]] | [[Exercise_Quantifiers#Scopal_Ambiguity|Return to Excercise]] | ||
Revision as of 00:12, 15 November 2013
1. For every person there is at least one person who loves him / her:
∀x (person(x) ⊃ ∃y (person(y) ∧ love(x,y)
Or, in restricted-quantifier notation:
∀x (person(x) : ∃y (person(y) : love(x,y)
2. There is one person that is loved by everyone:
∃y (person(y) ⊃ ∀x (person(x) ∧ love(x,y)
Or, in restricted-quantifier notation:
∀x (person(x) : ∃y (person(y) : love(x,y)