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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$\exists x P(x)$: There exists a student x such that x spends more than five hours every weekday in class. Show more…
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Let variable x represent students and y represent courses, and : U(y): y is an upper level course M(y): y is a math course F(x): x is a freshman A(x): x is a part time students T(x, y): student x is taking course y Write each statement using these predicates and any needed quantifiers. a. Every student is taking at least one course b. There is a part time student who is not taking any math course. c. Every part time freshman is taking some upper level course.
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