Let P(x) be the statement "x spends more than five hours every weekday in class," where the domain for x consists of all students. Express each of these quantifications in English. a) ?xP(x) b) ?xP(x) c) ?xP(x) d) ?xP(x)
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Let $P(x)$ be the statement "x spends more than five hours every weekday in class," where the domain for $x$ consists of all students. Express each of these quantifications in English. $$ \begin{array}{ll}{\text { a) } \quad \exists x P(x)} & {\text { b) } \forall x P(x)} \\ {\text { c) } \quad \exists x \neg P(x)} & {\text { d) } \forall x \neg P(x)}\end{array} $$
The Foundations: Logic and Proofs
Predicates and Quantifiers
Let P(x) be the statement "x spends more than five hours every weekday in class," where the domain for x consists of all students. Express each of these quantifications in English. • ∀xP(x). • ∃xP(x). • ∀x¬P(x). • ∃x¬P(x).
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Let $P(x, y)$ be the statement "Student $x$ has taken class $y,$ where the domain for $x$ consists of all students in your class and for $y$ consists of all computer science courses at your school. Express each of these quantifications in English. $$ \begin{array}{ll}{\text { a) } \exists x \exists y P(x, y)} & {\text { b) } \exists x \forall y P(x, y)} \\ {\text { c) } \forall x \exists y P(x, y)} & {\text { d) } \exists y \forall x P(x, y)} \\ {\text { e) } \forall y \exists x P(x, y)} & {\text { f) } \forall x \forall y P(x, y)}\end{array} $$
Nested Quantifiers
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