Translating an English statement to its logical equivalent Translate the sentence to its logical equivalent:
There are at least three people who are TA’s and have not taken the class
The domain is the set X. You may use the functions S(x), meaning that “x has taken the class” T(x), meaning that “x is a TA” and E(x,y), meaning that “x and y are the same person.”
I am confused between 
∃x,y,z not E(x,y) & not E(x,z) & not E(y,z) & T(x) & not S(x) & T(y) & not S(y) & T(z) & not S(z)
∃x,y,z not E(x,y) & not E(x,z) & not E(y,z) & (T(x) => not S(x)) & (T(y) => not S(y)) & (T(z) => not S(z))
I've checked their truth tables, these are not logically equivalent. But intuitively, they seem to be same. "There is a TA who hasn't taken the class". Where am I going wrong?

Intuitively they are actually not the same. $T(x) ⇒ \neg S(x)$ means "( if $x$ is a TA, then $x$ has not taken the class )", which says nothing about whether $x$ is a TA or not.
