The word “or” can be either “inclusive” or “exclusive.” That is to say, sometimes, it includes the possibility of both:
“It would be nice to have a Ferrari or a Porsche” doesn’t mean that wouldn’t be nice to have a Ferrari AND a Porsche. That’s the “inclusive” or – it means “At least one.”
On the other hand, contrast this with:
“Please put two packets of Sweet & Low or sugar in my coffee.” We can safely infer that I don’t want two packets of Sweet & Low AND two packets of sugar in my coffee. Unlike the Ferrari/Porsche example, in this case, it means “Exactly one.”
On the LSAT (which is to say, when dealing strictly with the logical context), “or” is always inclusive *unless you’re told otherwise, or the context makes the inclusive “or” impossible.* That’s why you’ll see, in certain logic games, rules like “The blue team includes Rob or Jeff, BUT NOT BOTH.” (emphasis added). If it didn’t say “but not both,” then it would be fine to put Rob AND Jeff on the blue team. In other words, “or” really means “and/or.”
I said that sometimes context makes that impossible. Let’s say we have a sequencing game involving a race, and there’s a rule that says, “Kim finishes in first place or third place.” Obviously, she can’t finish in both 1st place AND 3rd place, so by context, we have an instance of the exclusive “or.”
SO, getting back to your question, the answer “either F or L is played” is correct; however, you’re also correct in noting that they could BOTH be played. When Mike says either F or L is played, that doesn’t preclude the possibility of both. It’s the inclusive “or,” which it always is, unless it can’t be, or you’re told otherwise. So it’s one, or the other, or both being played. All of which is covered by the statement “F or L is played.”
Going back to your other question, yes…you’ve mistranslated (B). You’ve symbolized it exactly is if the word “only” were not in the sentence. The first thing I tell any LSAT class is that the most important word on the LSAT is “only.” Perhaps the simplest way to look at its effect is that “only” negates both sides of a conditional relationship. So the fact that the word “only” is there means that (B) isn’t:
NOT L –> F
L –> NOT F
One way to see this a little more clearly is to keep the structure of the statement while substituting content that you’re familiar with. For instance, passing the bar exam is a requirement of practicing law. So let’s use “practice law” instead of F, and “fail the bar exam” instead of L. Now, (B) would read:
“(She) will practice law only if she doesn’t fail the bar exam.” That’s a true statement. But now let’s look at the way you translated it:
“If she doesn’t fail the bar exam, she will practice law.” (Not L –> F). That’s no longer a true statement. She might pass the bar exam and go on to medical school. Or pass the bar exam but then fail the background check. Or fail to pay her bar dues. Passing the bar exam isn’t a guarantee of lawyerdom. But look what happens when you negate both sides:
“If she DOES fail the bar exam, she will NOT practice law.” Yup. That’s the one we want.
So basically, you got it half right – you translated the original statement correct; you just have to realize that the given correct answer agrees with you – “Or” is inclusive (except when…)
But watch out for the word “only”; if it weren’t there, (B) would, indeed, be a correct answer. But the fact that it is there makes a world of difference.
Hope this helps.