predicate logic ,writing in notation form

Question

The statement below should be rewritten in the form “ for all · · · x, · · · .”

"No computer scientists are unemployed" Answer Let computer scientists = CS unemployed=U

for all x element of CS, x is not an element of U.

Answer 1

Yes. That's one direction to go:

If we consider $C$ the set of all computer scientists and $U$ the set of unemployed persons, then $$\forall x(x \in C \rightarrow x \notin U)$$

---

We can alternatively use predicates, and designate the domain to be the set of all people.

Let $C(x)$ mean "$x$ is a computer scientist."

Let $U(x)$ meaning "$x$ is unemployed."

Then we have, $$\forall x\Big(C(x)\rightarrow \lnot U(x)\Big)$$