Let I(x) be the statement “x has an Internet connection”

Chapter 7, Problem 12E

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QUESTION:

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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QUESTION:

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.

ANSWER:

Solution :Step 1:In this problem we have to express the given statements using quantifiers.Where we given I(x) = “x has an internet connection ” and C(x , y) = “x and y have chatted over the internet ”.We know that the quantifiers:Negation “NOT” : Conjunction “AND” : “”Disjunction “” : “”If then “implies” : “ ”If and only if : “”For all “every one” : There Exists “any one” : “”The existential quantifiers of the negation is : This is logically equivalent to : So the negation for x and y have chatted over the internet written as “x has not chatted over the internet with y ”.

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