Answer to Question #293112 in Discrete Mathematics for Astrid

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

a) There exists a student who spends more than five hours every weekday in class.

b) All students spend 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.