Let I(x) be the statement \"x has an Internet connection\" and C(x,y) be the sta

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.

e. Sanjay has chatted with everyone except Joseph
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.
o. There are two students in the class who between them have chatted with everyone else in the class.

Explanation / Answer

Let S = the set of all students in your class. e. there exists a y in S such that not(C(Sanjay, y)) j.For all x in S there exists a y such that C(x,y) k. There exists an x in S such that l(x) and for all y in S not(C(x,y)) o. There exists x1, x2 in S such that for all y in S, C(x1,y) or C(x2,y). Dictionary: "there exists" = backwards 'E' "for all"= upside down 'A' "in"= epsilon not = sometimes I see a '~' or a sideways 'L' and= ^ or = 'v'

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