Quantified Propositions to English
I need help with this problem.
Let P(x, y) be x has been to y, where the domain of discourse for x is all students in this class, and the domain of discourse for y is all towns in Illinois. Express the following propositions in English.
a) ∃x ∀y P(x, y)
b) ∀y ∃x P(x, y)
I know a is There is a student in this class who has been to all towns in Illinois.
What is b?
Also - the next problem is for me to negate the above statements, can anyone help with that?