How to express in Propositional Logic

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If A(S;C) is the propositional function (predicate) and student S who takes course C receives an A grade and the domain is a set of student belonging to university x.

How to express "There are students belonging to x university with all A's" in symbolic form.

I express the basic proposition as S->C->A.I need to know whether this is right and also how to express the above condition in symbolic form.

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This isn't a question in propositional logic, but predicate logic.

You need to render the claim "There exists a student S such that for any course C, A(S,C)."

That means using quantifiers.