Translating a statement from plain English to a mathematical expression I did a logic exercise about which I have a question :
considering the booleans A : "Peter is a student" and B : "Julia is a student", what formula represents the statement "Peter is a student if Julia is a student"?
I answered $B\Rightarrow A$ but I was said that the statement does not mean that Julia being a student implies Peter being one, but instead that Peter cannot be a student if Julia is not one and therefore the correct answer should be $\lnot B \Rightarrow \lnot A$. However, I assumed that the verb "is" in the first clause implies that whatever happens, if Julia is a student then it is also Peter's case. I would have phrased the second formula as such : "Peter could be a student if Julia were one".
How should the statement be written? 
 A: If you consider that "Peter is a student if Julia is a student" implies that : "If Julia is a student, then Peter is a student" , but Peter may be a student even if Julia isn't , which I think is the most correct,  $B⇒A $ is the apropriate representation. 
If you defend that the statement means $¬B⇒¬A\ $ then by the reciprocal (you can prove it using a truth table or using De Morgan laws) we can write $A⇒B$ and the english representation may be :
"Peter can't be a student if Julia isn't." , or "Only if Julia is a student Peter is a student", or even "If Peter is a student, then Julia is one".
If you want to convey both meanings, that "Peter is a student if and only if Julia is a student", you can even represent it as $A \Leftrightarrow B$ , obviously because if and only if is the logical "equivalent", and also mathematicly because $B⇒A$ and $A⇒B$.
But how should the statement be written ? Like Dave Renfro said, it is standard to translate "$A$ if $B$" in english into "$B⇒A$" in mathematical logic. The only thing I can think of to improve understanding is that you include a "then" in the statement, "If Julia is a student, then Peter is a student" , and that should reinforce the idea of $B⇒A$. 
P.S. Your english representation of the second formula is not on point, and you commit the same "error" as the people who formulated the 2nd formula. "Peter could be a student if Julia were one" doesn't implie that Peter couldn't be a student if Julia wasn't one. It can't be represented logicly as $¬B⇒¬A\ $, or even   $B⇒A\ $, because it doesn't refer to what Peter is or can't be, just what he could be. It is sort of a tautology, because we can always "assign" Truth value to it (without any more statements). A better representation would be "Peter could only be a student if Julia were one"
