e) Explain, in intuitive terms, why "(3! x ES) (p(x))" means the same thing as "(3x ES) [p(x) and ([V u ES] [p(u) ⇒ u = x])]".

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 "There is a student in your class who has chatted with everyone in your class over the Internet." A aXvy C(x, y) В 3Xay(x = y ^ vz ¬(C(x, z) ^ C(y, z))) эхзу(х %3D у л vz(C(x, z) v C(у, z))) D) aXvy(x = y I(y))

1)     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.  Jerry has an Internet Rachel has chatted over the Internet with Jan and Sharon have never chatted over the Everyone in the class has chatted with Sanjay has not chatted with everyone except Someone in your class does not have an Internet Not everyone in your class has an Internet Exactly one student in your class has an Internet Everyone except one student in your class has an Internet Everyone in your class with an Internet connection has chatted over the Internet with at least one other student in your Someone in your class has an Internet connection but has not chatted with anyone else in your There are two students in your class who have not chatted with each other over the There is a student in your class who has…

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. The quantification of this statement "Exactly one student in your class has an Internet connection." is avy(x = y I(y)). A True False

How many logical operators which take three arguments? That is, how many functions of type f : B³ → B, where B = {0, 1}?