3a

T(a,b) = Student a likes TV show b where the domain for a is the students in the class and the domain for b is the shows currently airing on TV

Translate:

∀s∃t∃u(T(s,u)→¬T(t,u))

T(s,u) = all students s like a TV show u

or everybody likes a TV show

¬T(t,u) =  it is not the case that a student t likes the TV show u

its not true that one student likes the TV show

(T(s,u)→¬T(t,u))

if everybody likes a TV show, then its not true that one student likes the TV show,

* can this be translated into :

if everybody likes a TV show, then there is not one student who doesnt like the TV show?

3b

use quantifiers and variable to translate the following prop

there is a TV show that everybody likes.

on the test i put this:

∀x∃y (T(x,y))

*should it be

∃y∀x (T(x,y))?