In the Riverview Building, every apartment that has a balcony also has a fireplace. None of the apartments with balco...

Mehran on August 30, 2017

@Genadel thanks for your message. Let's take a closer look at the stimulus here.

Premise: "In the Riverview Building, every apartment that has a balcony also has a fireplace."

B ==> F
not F ==> not B

Premise: "None of the apartments with balconies is a one-bedroom apartment."

B ==> not 1BR
1BR ==> not B

Conclusion: "So none of the one-bedroom apartments has a fireplace."

1BR ==> not F
F ==> not 1BR

Notice the flaw here.

We know that one-bedrooms do not have balconies, i.e. 1BR ==> not B.

Not having a balcony, however, is necessary to not having a fireplace, i.e. not F ==> not B.

The argument is clearly mistaking necessary for sufficient here, i.e. not B ==> not F, to then conclude that "none of the one-bedroom apartments has a fireplace."

1BR ==> not B ==> not F

Let's take a look at (C) now:

"no dog has fur since every cat has fur and no cat is a dog"

Premise: "every cat has fur"

C ==> F
not F ==> not C

Premise: "no cat is a dog"

C ==> not D
D ==> not C

Conclusion: "no dog has fur"

D ==> not F
F ==> not D

This is the exact same flaw. We know that no dogs are cats, i.e. D ==> not C.

But not being a cat is necessary to not having fur, i.e. not F ==> not C.

So the argument here is once again mistaking necessary for sufficient, i.e. not C ==> not F.

D ==> not C ==> not F

Therefore, (C) would be the correct answer.

Hope that helps! Please let us know if you have any other questions.