Translating English to logical predicate

Question

What is the translation of this sentence to logical predicate "A student in your class has taken a course in logic programming"?

Answer 1

Consider $U$ to be the collection of all the students in the class that you mentioned, and let $P(x)$ be the expression $P(x) = \text{ “Student $x$ has taken a course in logic programming.”}$ Then your statement is of the form

$$(\exists x \in U):[P(x)].$$

If the domain is to be all people in the world (say $W$) then you have to define a expression $S(x)$ to be $S(x) = \text{ “Person $x$ is a student in your class.”}$ Then your statement is of the form

$$(\exists x \in W):[S(x) \wedge P(x)].$$

(Since the statement can be rephrased as “There is a person that is in your class and has taken a course in logic programming”.)