#21 - Guidelines for constructing new Bonjour hotels:

[Administrator]

Complete Question Explanation

Must Be True, Principle. The correct answer choice is (B).

This stimulus gives us two conditional statements involving the construction of new Bonjour hotels:

RFCSI or LH RFHSI

RHHS ~RFCSI

It's typically a good idea to write out the contrapositives of conditional statements as well:

~RFHSI ~RFCSI + ~LH

RFCSI ~RHHS

With Must Be True and Most Strongly Supported questions like these, it is crucial to be vigilant against answer choices that are logically invalid. Use your conditional diagrams, and remember that you can only go from left to right.

Answer choice (A): The stimulus made no connection between a luxury hotel and a radiant floor cooling system, so we can safely skip this answer.

Answer choice (B): This is the correct answer choice. Yes! This is perfectly supported the stimulus. Because it's a luxury hotel, we should have a radiant floor heating system installed, but because it will be in a region that has high humidity throughout the year, we should not install a radiant floor cooling system.

Answer choice (C): This answer choice commits both a Mistaken Negation and a Mistaken Reversal: it negates the sufficient condition of being a luxury hotel and treats the necessary condition of a radiant floor heating system as sufficient to justify its conclusion. Hard pass.

Answer choice (D): This is refuted by the first conditional statement: if the hotel will be a luxury hotel, it should definitely have a radiant floor heating system installed, even though this answer choice is correct about the cooling system.

Answer choice (E): This answer choice is correct about having a heating system because it's a luxury hotel, but does a Mistaken Negation of the second conditional and is thus incorrect.

[sidneythomas1222@gmail.com]

Hi PowerScore,

I see why B is correct, but I'm having trouble figuring out why E is incorrect. I mapped out the reasoning like this:

Floor heating (FH)-----> Floor cooling (FC ) or Luxury Hotel (L)------------------> Low Humidity (LH)


With E, both the necessary conditions are met for FH and FC (low humidity and luxury hotel). I wasn't the most confident mapping out the statements here, as the necessary conditions came after the "if." Thank you for all of your help!

[Adam Tyson]

It looks like you started out with a Mistaken Reversal of the first conditional rule, Sidney. The "if" in that first sentence establishes that the Sufficient Condition is Radiant Floor Cooling or Luxury Hotel, while the Necessary Condition is Radiant Floor Heating. So the first rule is:

RFC

or RFH

LH

And the second conditional rule is:

HH (high humidity) RFC

From these two rules you can see that there is no way to ever prove that a hotel should not have radiant floor heating, because to get there would require Mistaken Negation of the first rule. Answer D also makes a different sort of mistake, which is that it violates the first conditional rule by having the Sufficient Condition (luxury hotel) occur and claiming that the Necessary Condition (radiant floor heating) should not occur. That means answer D CANNOT be true! It was half right - the hotel should not have radiant floor cooling - but half wrong, and that's enough to make it a loser.

[gabyd33]

Hi Adam, could you please clarify your explanation? Here is my diagram of the conditional relationship in the stimulus.

RCS = radiant floor cooling system is to be installed
RHS = radiant floor heating system is to be installed
LH = hotel is to be a luxury hotel
HHS = hotel is located in a region that tends to have high humidity during the summer

RCS or LH RHS
The contrapositive of this statement is RHS RCS & LH

HHS RCS
The contrapositive of this statement is RCS HHS

Here is my diagram of answer choice (B).

LH RHS
HHS RCS

Here is my diagram of answer choice (E). From my reading of the conditional relationship, the reasoning in answer choice (E) was a Mistaken Reversal of the relationship between HHS and RCS so I eliminated it.

LH RHS
HHS RCS

Did I diagram the stimulus correctly? And did I answer correctly for the right reasons? Thanks in advance for the help.

[katehos]

Hi gabyd33!

I'm not Adam, but I can help answer your question You did a great job with your diagram of the stimulus as well as the answer choices! Additionally, you eliminated (E) for the correct reason: part of it is a Mistaken Reversal of the contrapositive of the second rule (or a Mistaken Negation of the original conditional of the second rule).

Keep up the good work!
Kate

[lounalola]

I was in between B and E for this question and I ended up choosing E. How would I properly diagram answer choice E so that I could see the mistake in the answer?

[Adam Tyson]

As shown earlier in this thread, answer E includes two conditional claims, one of which matches the stimulus and one of which mistakenly negates a claim in the stimulus.

The stimulus tells us that luxury hotels should have radiant floor heating. E does exactly that:

LH RFH

The stimulus also tells us that if there is high humidity in the summer, the hotel should not have radiant floor cooling:

HHS RFC

But answer E negates this, saying since this hotel will be in a place with low humidity, it should have radiant floor cooling:

HHS RFC

As you can see, that portion of answer E is a Mistaken Negation of the stimulus, so you can't say that it is supported by the stimulus.