# Which one of the following could be a complete and accurate list of the stations that stay open?

Shirley on November 23, 2019

Game Set Up

Irina on November 23, 2019

@shirlmeji09,

Happy to help. This is an in-out grouping game that requires us to determine which of the six stations - L M N P Q R - will be closed and which will stay open. The following rules apply:

(1) N & R cannot both close
This rule tells us that at least one of these stations or both must be on the "open" list.
This rule also tells us that if one of them closes the other must stay open:
N c -> R o
R c-> No

Open Close
N/R

(2) If N stays open, then L must also stay open.
N o -> L o

This rule also allows us to infer that if L closes, then N must close as well and then R must stay open per rule (1).

L c-> N c -> R o

Open Close
R L N

(3) If R stays open, then M must also stay open.
R o -> M o

This rule allows us to infer that if M closes, then R must close, and N and L must stay open per rules 1 & 2.

M c -> R c -> N o -> L o

Open Close
N L M R

Open Close
R M

or a short version of this logical chain is:

M c -> L o

The relationship between M & L is thus similar to N & R, one of these stations must stay open.

(4) L & R cannot both stay open.

This rule tells us that one or both of the stations must be closed. We can also infer that if L stays open, R must close, and if R stays open, L must close.

R o -> L c
L o - > R c

We can thus infer that R & N cannot both stay open, thus one of them must stay open and one must close, resulting in the following scenarios:

Open Close
R M L N

Open Close
N L /M R /M

Note that M could still be open in the second scenario where R is closed.

P and Q are free variables in this game and could be both closed, both stay open, or one of them could be closed and one could stay open..

The question asks us which of the following could be a complete and accurate list of the stations that stay open. From the scenarios above, we can tell that an open list must either include:
RM
NL or
NLM

We can eliminate (A) because it fails to include N, (B) because it fails to include M, (C) because it fails to include L, and (E) because L & R cannot both stay open per rule (4)

We can thus conclude that (D) is the correct answer - M & R are open along with the free variable Q per our scenario 1.

Let me know if this makes sense and if you have any other questions.