Translation of sentence into logical proposition

Translation of sentence into logical proposition

Given the sentence: "You can access the internet only if you are a
computer science major or you are not a freshman" and functions:
a = you can access the internet
b = you are a computer science major
c = you are a freshman
we need to translate into a logical proposition.
My intuitive approach is to say (b v ~c) -> a.
However, the solution suggested is a -> (b v ~c).
Are these two equivalent in the sense that the proposition was really an
iff statement? If this is the case, why wasn't it translated to [a -> (b v
~c)] ^ [(b v ~c) -> a]?