Symbolize the following sentences with the given symbolization key

Symbolize the following sentences with the given symbolization key.

UD: All currently living people. b: Barbara Ey: y will travel to Europe. Py: y will travel to Portugal. Hx: x will stay home. Vxy: x will visit y.

UD stands for the domain of discourse (everything in the world that we can refer to). w, x, y, and z are variables. And I think we are supposed to use quantifiers.

(a)Any person will travel to Europe only if that person visits Barbara.

(b)If one person travels to Portugal and another doesn't travel to Europe then neither of those people will visit the other.

(c)If one person visits another, then either both travel to Europe or both stay home.

(d)For everyone who visits Portugal, there is someone that doesn't visit Europe and whom the first person doesn't visit.

For sentence a, am I using a universal quantifier to refer to the people who will travel to Europe and who will visit Barbara?

For sentences b-d, am I supposed to include that person x doesn't equal person y when referring to the different people. For example, for b, do I need to include that the person traveling to Portugal and the person not traveling to Europe are not the same people?

In sentence d, what does "whom the first person doesn't visit" mean? Who is the first person?

Any help and final answers would be very appreciated.

For sentence a, am I using a universal quantifier to refer to the people who will travel to Europe and who will visit Barbara?

Any person will travel to Europe only if that person visits Barbara

Yes, you quantify the person.

"For all persons (eg. $y$) it holds that: $y$ will travel to Europe iff $y$ visits Barbara (ie. $b$)."

For sentences b-d, am I supposed to include that person x doesn't equal person y when referring to the different people. For example, for b, do I need to include that the person traveling to Portugal and the person not traveling to Europe are not the same people?

(b)If one person travels to Portugal and another doesn't travel to Europe then neither of those people will visit the other.

Indeed you do.   The natural language sentences implicitly suggests that the persons are distinct, but the symbolic representation needs to be explicit about this.

In sentence d, what does "whom the first person doesn't visit" mean? Who is the first person?

(d)For $\underline{\text{everyone}}$ who visits Portugal, there is someone that doesn't visit Europe and whom the first person doesn't visit.

The first person mentioned.