Is this really "correct" and unambiguous?

Question

For one of my beginning CS classes, we are going over "truth functional logic."

My question pertains to English translations. Note that ^ is AND; v is (inclusive)OR; ~ is NOT. -> is IF

Well, we had this: "RENT being paid is a necessary condition for staying in BUSINESS"

RENT -> BUSINESS

Whenever we graded everything this was wrong. I asked the teacher why and she said nothing more then that "if there is no then in the sentence, then the antecedent is always last"

I would like some more explanation as to how this is wrong. And how the sentence is not ambiguous. Something more than "there was no then so it's always this way."

Also, a side note: Where did the IF boolean operator come from? I've never heard of such an operator that is basically equivalent in Cish code to a==true?b:true. I have a very hard time grasping it's usage.

edit: The correct answer was

BUSINESS -> RENT

Answer 1

If you pay rent, you're not necessarily in business. Rent !(->) Business.

However, if you're in business, you must pay rent. Business -> Rent.

Answer 2

I think it should have been written:

BUSINESS -> RENT

"If you're staying in business, then you're paying rent."

P -> Q

can be stated "P implies Q," "If P, then Q," or "Q if P."