This is an excerpt from my textbook(Discrete Mathematics and Its Applications 7th edition)
When I tried doing this example on my own, my answer was "There is a student x in this class and that student x has visited Mexico". Would that be logically equivalent or the same as the answer that the author came to? They both express the idea that there exists a student in that class that has visited Mexico. I am just not sure if the author went out of his way to use with the property and not just and?
It's the same thing, but this shouldn't be about playing with words. One needs to do this more formally:
Let $A(x)$ be the predicate "$x$ is a student in this class" and let $B(x)$ be the predicate "$x$ has visited Mexico". Now one can write the sentence as $$\exists x, A(x)\land B(x).$$