Examples if px denotes x 0 and domain is the integers

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Unformatted text preview: r.” —༉  The two most important quantifiers are: —༉  Universal Quantifier, “For all,” symbol: ∀ —༉  Existential Quantifier, “There exists,” symbol: ∃ —༉  We write as in ∀x P(x) and ∃x P(x). —༉  ∀x P(x) asserts P(x) is true for every x in the domain. —༉  ∃x P(x) asserts P(x) is true for some x in the domain. Universal Quan$fier —༉  ∀x P(x) is read as “For all x, P(x)” or “For every x, P(x)” Examples: If P(x) denotes “x > 0” and domain is the integers, then ∀x P(x) is false. If P(x) denotes “x > 0” and domain is the positive integers, then ∀x P(x) is true. If P(x) denotes “x is even” and domain is the integers, then ∀ x P(x) is false. Existen$al Quan$fier —༉  ∃x P(x) is read...
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