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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". Express each of the following statements in terms of I(x) and C(x,y), quan- tifiers, and logical connectives. Let the universe of discourse for the variables x and y consist of all students in your class. Put the appropriate letter next to the corresponding symbolic form. 1. (C(Rachel, Chelsea) 2. xy(y #x^-C(x,y))) 3. C(Jan, Sharon) 4. x(1(x)^Vy(1(y) →y=x)) 5. Vx-C(x,Bob) 6. Ex-1(x) 7. xy(x^₂-(C(x,z) AC(y,z)) —8. Vx(1(x)) → ‡y(xy^C(x,y)) a) Rachel has not chatted over the internet with Chelsea. b) Jan and Sharon have chatted over the internet. c) No one in the class has chatted with Bob. d) Someone in your class does not have internet connection. e) There are two students in your class who have not chatted over the internet. f) Exactly one student in your class has an internet connection. g) Everyone in your class with an internet connection has chatted over the internet with at least one other student in your class. h) There are at least two students in your class who have not chat- ted with the same person in your class.

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". Express each of the following statements in terms of I(x) and C(x,y), quan- tifiers, and logical connectives. Let the universe of discourse for the variables x and y consist of all students in your class. Put the appropriate letter next to the corresponding symbolic form. 1. (C(Rachel, Chelsea) 2. xy(y #x^-C(x,y))) 3. C(Jan, Sharon) 4. x(1(x)^Vy(1(y) →y=x)) 5. Vx-C(x,Bob) 6. Ex-1(x) 7. xy(x^₂-(C(x,z) AC(y,z)) —8. Vx(1(x)) → ‡y(xy^C(x,y)) a) Rachel has not chatted over the internet with Chelsea. b) Jan and Sharon have chatted over the internet. c) No one in the class has chatted with Bob. d) Someone in your class does not have internet connection. e) There are two students in your class who have not chatted over the internet. f) Exactly one student in your class has an internet connection. g) Everyone in your class with an internet connection has chatted over the internet with at least one other student in your class. h) There are at least two students in your class who have not chat- ted with the same person in your class.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.3: Solving Problems Involving Inequalities
Problem 28E
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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". Express each of the following statements in terms of I(x) and C(x,y), quan- tifiers, and logical connectives. Let the universe of discourse for the variables x and y consist of all students in your class. Put the appropriate letter next to the corresponding symbolic form. 1. (C(Rachel, Chelsea) xy(yx^¬C(x,y))) 2. 3. C(Jan, Sharon) 4. Ex(1(x) ^Vy(1(y) →y=x)) 5. Vx-C(x,Bob) 6. Ex-1(x) 7. x³yyx^z-(C(x,z) AC(y,z)) 8. Vx(1(x))→→y(xy^C(x, y)) a) Rachel has not chatted over the internet with Chelsea. b) Jan and Sharon have chatted over the internet. c) No one in the class has chatted with Bob. d) Someone in your class does not have internet connection. e) There are two students in your class who have not chatted over the internet. f) Exactly one student in your class has an internet connection. g) Everyone in your class with an internet connection has chatted over the internet with at least one other student in your class. h) There are at least two students in your class who have not chat- ted with the same person in your class.
Transcribed Image Text: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". Express each of the following statements in terms of I(x) and C(x,y), quan- tifiers, and logical connectives. Let the universe of discourse for the variables x and y consist of all students in your class. Put the appropriate letter next to the corresponding symbolic form. 1. (C(Rachel, Chelsea) xy(yx^¬C(x,y))) 2. 3. C(Jan, Sharon) 4. Ex(1(x) ^Vy(1(y) →y=x)) 5. Vx-C(x,Bob) 6. Ex-1(x) 7. x³yyx^z-(C(x,z) AC(y,z)) 8. Vx(1(x))→→y(xy^C(x, y)) a) Rachel has not chatted over the internet with Chelsea. b) Jan and Sharon have chatted over the internet. c) No one in the class has chatted with Bob. d) Someone in your class does not have internet connection. e) There are two students in your class who have not chatted over the internet. f) Exactly one student in your class has an internet connection. g) Everyone in your class with an internet connection has chatted over the internet with at least one other student in your class. h) There are at least two students in your class who have not chat- ted with the same person in your class.
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