# If exactly two of the stations stay open, which one of the following must close?

on January 6, 2019

How do you set this question up

I got a few questions on this wrong. How do you set this up

3 Replies

Ravi on January 7, 2019

@reganashley5991,

Happy to help. Which questions did you miss? Let's walk through the setup.

We're told that the operator of a passenger railway system needs to
close at least one of its stations. Six stationsâ€”L, M, N, P, Q, and
Râ€”are being considered for closure.

This game is an in/out group game. Since the stations that are being
closed are the ones that are being "chosen," let's make those our "in"
group since we're selecting them.

The rules are

1) N - >/R (N without a slash means it's closed since we're choosing
it; R with a slash [/R] means it's open)

2) /N - >/L

3) /R - >/M

4)/L - >R

Now, let's look at how these rules interact with one another.

Rules 1 and 4 can be combined, so N - ->/R - ->/M

Rule 4's contrapositive is /R - >L, so this can be branched onto the
chain directly above.

Rule 2's contrapositive is L - >N. Combining this with Rule 4 and the
chain above, we see that L, N, and /R are all in biconditional
relationships with each other. L and N are always together, L and /R
are always apart, and N and /R are always apart. This will allow us to
split this game into two different boards.

For our two sub game boards, let's put N and L in the closed (in)
group in the first one:

Closed (In) Open (Out)
N R
L M

Our floating game pieces are P and Q; they can go wherever in this game board.

The reason that M is with R is because if R is open (out), then M is
also open (out)

In our second sub game board, let's put N and L in the open (out) group:

Closed (In) Open (Out)
R N
L

Our floating game pieces are M, P, and Q; they can go wherever in this
game board. The reason that M is a floating game piece in this board
is that in this game board, the sufficient condition for Rule 3 has
been failed, so M can go wherever.

Does this setup help you? Let us know which specific questions you
were struggling the most with, and we can walk through them with you.
Also, if you have any additional questions, feel free to reach
outâ€”we're here to help!

Serra on July 15, 2019

Explanation for question 5 please. There is no video explanation for this game.

"If exactly two of the stations stay open, which one of the following must close?"

Thanks!

Ravi on July 31, 2019

@msaber,

Let's take a look at question 5.

We know exactly two stations are open. This means that four are closed.

In looking at the rules, we can make some conditional logic chains

N - >/R - >M

/R - >L - >N

Notice how there's a lot of interrelation here. If N is in, then L is
too. If N is out, then R must be in because if R is out, then L and N
would both have to be in.

If L is in, then N must be in too.

If M is in, then R must be in and N and L must be out.

Based on looking at these chains, we see that N, L, R, and M don't
have to be out. They can all either be in or out. However, notice that
P and Q are not in these chains. If we put P or Q in, then we run into
big problems because there's not enough space. Looking at the answer
choices, we see that P isn't listed, but Q is, so we know that (D) is