Let I(x) be the statement “x has an Internet connection.” Let C(x,y) be the stat

Question

Let I(x) be the statement “x has an Internet connection.” Let C(x,y) be the statement “x and y have chatted over the internet.” Let the domain of x and y consists of all students in a class. Use quantifiers to express each of these statements.

a). Carlos has no internet connection.

b). Neither Alice nor Bob has chatted with Carlos over the internet with at least one other student in the class.

C). Everyone in the class with an internet connection has chatted over the internet with at least one other student in the class.

D). Everyone who has not chatted with Bob over the internet did not have an internet connection.

Explanation / Answer

l(x) = "x has an internet connection" C(x,y) = “x and y have chatted over the internet.”

a) Carlos has no internet connection : ~l(Carlos)

b) "Neither Alice nor Bob has chatted with Carlos over the internet".

=> ~C(Alice,Carlos) ^ ~C(Bob,Carlos)

c) "Everyone in the class with an internet connection has chatted over the internet with at least one other student in the class."

x l(x) -> C(x, y)

d) "Everyone who has not chatted with Bob over the internet did not have an internet connection"

x ~C(x,Bob) -> ~l(x)

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