The domain for the first input variable to predicate T is a set of students at a university. The domain for the second input variable to predicate T is the set of Math classes offered at that university. The predicate T(x, y) indicates that student x has taken class y. Sam is a student at the university and Math 101 is one of the courses offered at the university. Give a logical expression for each sentence. a) Every student has taken at least one math class.
b) Every student has taken at least one class other than Math 101.
c) There is a student who has taken every math class other than Math 101.
d) Everyone other than Sam has taken at least two different math classes.
e) Sam has taken exactly two math classes.