#17 - Global, Rule Substitution

[Adam354]

I do not understand the difference between

L closes M must be in
&
L closes R must be in

L out -> N out -> R in -> M in

Therefore, both L out R in, and L out M in seem to have the same effect.

So A & B both seem correct. What am I missing?

[Adam Tyson]

What you're missing there, Adam, is that the question told us to replace the rule about R and M. If that rule is removed from the game, M becomes a random variable with no rules affecting it. Answer choice B does nothing to change that, so M remains random, and in your scenario there is no reason that M must be in. Whatever else the correct does, it must have some direct impact on M!

[SGD2021]

Hello, I am confused between A and D.

A) says that Lc-->Mo. We know that if L is closed, then N is closed and if N is closed then R is open. Why does this mean Ro--> Mo?

D says Lo-->Mc. We know that if L is open then R must be closed. So why can't this be read as Mc-->Rc (which would be the contrapositive of the rule we're replacing?) . Why do we read it as Rc-->Mc?

[Robert Carroll]

SGD2021,

To your first point - use the last rule:

If R is open, L is closed (last rule)

If L is closed, M is open (answer choice (A))

By a chain of conditionals, if R is open, M is open, which is what we wanted.

To your second point:

Answer choice (D) isn't even true, much less a good substitute for the third rule. Look at question #15, answer choice (C) - this is a wrong answer for question #15, and says "M stays open". In other words, we already know from this answer that L and M could be open at the same time - so what answer choice (D) is saying for question #17 isn't true at all.

It looks like you're doing the Mistaken Reversal of "Lo-->Mc". You say that we know that if L is open, then M is closed. And if L is open, R is closed. So if L is open, two different necessary conditions happen - but they're both necessary conditions. They don't connect to each other at all.

Robert Carroll