Exercise # 1.5 Q12 ( Nested Quantifiers)|| Rosen Discrete Mathematics 7th Edition|| M.Owais

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12. Let I (x) be the statement “x has an Internet connection”
and C(x, y) be the statement “x and y have chatted over
the Internet,” where the domain for the variables x and y
consists of all students in your class. Use quantifiers to
express each of these statements.
a) Jerry does not have an Internet connection.
b) Rachel has not chatted over the Internet with Chelsea.
c) Jan and Sharon have never chatted over the Internet.
d) No one in the class has chatted with Bob.
e) Sanjay has chatted with everyone except Joseph.
f ) Someone in your class does not have an Internet connection.
g) Not everyone in your class has an Internet connection.
h) Exactly one student in your class has an Internet connection.
i) Everyone except one student in your class has an Internet connection.
j) Everyone in your class with an Internet connection
has chatted over the Internet with at least one other
student in your class.
k) Someone in your class has an Internet connection but
has not chatted with anyone else in your class.
l) There are two students in your class who have not
chatted with each other over the Internet.
m) There is a student in your class who has chatted with
everyone in your class over the Internet.
n) There are at least two students in your class who have
not chatted with the same person in your class.
o) There are two students in the class who between them
have chatted with everyone else in the class

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