# If exactly three friends appear together in a photograph, then each of the following could be true EXCEPT:

on July 31 at 10:33PM

C

I understand why A must be false, but why is it also not the case that C must be false? If W and S are in, then wouldn't we need U and Y as well which would make it 4 friends?

Shunhe on August 1 at 03:33AM

Hi @elawrencehenderson,

Thanks for the question! So let’s take a close look at those rules that you’re referring to to see if (C) must be false or not. Let’s say that W and S are in.

So you’re looking at the second rule, which says that S appears in every photograph that U appears in, in order to conclude that U would have to be in too. But is this the case? How can we phrase this rule in “if-then” language? Well, it means that if U is in a photograph, then S is in it. In other words, this is

U —> S

So what if S is in the photo? Does that mean U is in it? No, that’s a case of a mistaken reversal. S is in the necessary condition, not the sufficient condition! And it makes sense. Just because S is in every photo U is in, doesn’t mean that U is in every photo that S is in! S can be in photos without U, even though U can’t be in photos without S. And so actually, U doesn’t have to be in the photo. And that’s enough to show that (C) could be true, since in that case, a possible combination would be W, S, and Y.

Hope this helps! Feel free to ask any other questions that you might have.