Ok, I am required to use quantifiers and predicates with more than one variable

Question

Ok, I am required to use quantifiers and predicates with more than one variable to express these statements.

I am not completely sure how to do it...

14d) All students in this class have learned at least one programming language:
Ax(Ex L(x, y)) Not sure if this is correct though...A(x) is universal quantifier, and E(x) is existential quantifier.

14e) There is a student in this class who has taken every course offered by one of the departments in this school: NO CLUE! It actually doesn't sound too difficult, but I'm not sure how I'm supposed to do the variables and stuff...

any help would be greatly appreciated thanks!

Explanation / Answer

#1) x = student in this class y = learned a programming language L(x,y) = x has learned a programming language for every student in this class (Ax) there exists a language (Ey) such that L(x,y) is true. So the statement should be AxEy(L(x,y,)) #2) x = a student in this class y = a given department L(x,y) = a student has taken a class in a given department There exists a student (Ex) that for every department (Ay) such that L(x,y) is true. So that statement should be ExAy(L(x,y))

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