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Unformatted text preview: Nested Quantiﬁers:
Table 1 on Page 53 Statement When True? When False? ∃x∀yP (x, y ) There is an x for which For every x, there is a y P (x, y ) is true for every y . for which P (x, y ) is false. ∀x∃yP (x, y ) For every x, there is a y for which P (x, y ) is true. There is an x such that P (x, y ) is false for every y . ∀x∀yP (x, y ) P (x, y ) is true ∀y ∀xP (x, y ) for every pair x, y There is a pair x, y for which P (x, y ) is false. ∃x∃yP (x, y ) There is a pair x, y ∃y ∃xP (x, y ) for which P (x, y ) is true. P (x, y ) is false for every pair x, y . ...
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This note was uploaded on 04/06/2010 for the course LAPS MATH 1190 taught by Professor Adachan during the Spring '10 term at York University.
 Spring '10
 ADACHAN

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