What is the fallacy in my reasoning of this sentence-to-first-order-logic-problem? Given predicates


*

*Occupation(p,o) (Person p has job o)

*Client(p1, p2) (Person p1 is a client of person p2)


And constants:
•   Occupations: Lawyer, doctor, officer
•   Persons: Emily, Joe
And sentence:


*

*There exists a lawyer of which all its clients are doctors.


I then translated the above sentence in first-order logic and came up with this:
∃x[Occupation(x,lawyer) ⟶ ∀y[Occupation(y,doctor) ∧ Client(y,x)]]
This reads (according to me): There exists an X such that if X is a lawyer, then all Y's are a customer of X and they're doctors. 
However, peeking at the answers, I found that the only solution was:
∃x[Occupation(x,lawyer) ∧ ∀y[Client(y,x) ⟶ Occupation(y, doctor)]]
This reads (according to me): There exists an X such that if X is a lawyer and all Y's are a client of X, then they are all doctors. I feel like this doesn't express the sentence correctly.
I'm stumped as to why my answer is incorrect! I can't figure out the logical difference between those two sentences and English isn't my main language (so maybe that's where the problem lies?). What is the fallacy in my reasoning? 
 A: You are correct in your translation of your sentence, but this does not correspond to the initial plain English sentence.
This is how I would translate your sentence:

There exists X such that if X is a lawyer then for every Y, Y is  doctor and a client of X

Pretty much the same as you translated it. What does this mean though? First of all notice that after there exist X we have an if. This means that the sentence is trivially true (since X can be not a lawyer, and the sentence is still true). So you want to start with a statement that X is a lawyer and then add more conditions. Furthermore, let's assume we have X being a lawyer, what does the rest of the sentence mean? It means that there is a lawyer that has all people as clients (including themselves) and all people are doctors. So if there are 10 people in our universe, then one is a lawyer and all are doctors and clients of his/hers. The initial plain English statement of course just meant that, for example, one lawyer just has 2 clients and both of them are doctors. 
Furthermore you are not correct in your translation of the book sentence. Here's my translation:

There exist X such that X is a lawyer and for every Y, if Y is a client of X, then Y is a doctor.

This is the same as the initial plain English statement. See how it makes the definite statement that X is a lawyer and then continues with the conditional.
