Question

 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) ∃x ¬P(x) d) ∀x ¬P(x)

Answer 1

Solution:

(a) There exists a student who spends more than five

hours every weekday in class.

(b) Every student spends more than five hours every weekday in

class.

(c) There exists a student who does not spend more than five hours

every weekday in class.

(d) Every student does not spend more than five hours every weekday

in class.