This is my first assignment on these, so I would greatly appreciate your help.
Translate the following into predicate calculus. For each answer, also state the assumed universe of discourse.
a) "Anyone who was an ancient Roman citizen and tried to kill Caesar was not loyal to Caesar."
Ex(R(x) & k(x)) -> ~L(x)
R(x) = x is a Roman citizen, k(x) = x is tried to kill Caesar, L(x) = x is loyal to Caesar
b) "All cats which are calico, are female."
Ax(C(x) & O(x)) -> F(x)
C(x) = x is a cat, O(x) = x is calico, F(x) = x is female
c) "Some Texans have never left the state of Texas."
~Ax(T(x) & L(x))
T(x) = x is a Texan, L(x) = x is left Texas
Is the universe of discourse kind of like the "key" for the variables, as I included?