If there are any inspired performances in the concert, the audience will be treated to a good show. But there will n...

Nina on July 1, 2014

Trouble with transitive property

I am not able to make the conclusion drawn by the transitive property for answer choice A. I diagrammed the above set of facts as follows: P: IP - >GS Not GS - > Not IP P: Not GS - > Not SL GS - > SL P: SL - > UMR Not UMR - > Not SL So I see that from using the transitive property you can deduce: - IP - > GS - Not GS - > Not IP & Not SL How can you conclude Not SL then Not IP and visa versa?

9 Replies

Melody on July 18, 2014

Sorry for the delay! Let's diagram.

"If there are any inspired performances in the concert, the audience will be treated to a good show."

P1: IPC ==> GS
not GS ==> not IPC

"But there will not be a good show unless there are sophisticated listeners in the audience,"

(Remember that an "unless" introduces the necessary condition. The rest of the sentence is first negated and then makes up the sufficient condition. This is where your diagram went astray. Keep this rule in mind and you won't get stuck on an "unless" statement again. We can rewrite this: If there will be a good show, then there are sophisticated listeners in the audience.)

P2: GS ==> SL
not SL ==> not GS

"and to be a sophisticated listener one must understand one's musical roots."

P3: SL ==> UMR
not UMR ==> not SL

Answer choice (A) states: "If there are no sophisticated listeners in the audience, then there will be no inspired musical performance sin the concert."

(A) not SL ==> no IPC
IPC ==> SL

Okay, let's start with the contrapositive of P2. We have not SL ==> not GS, which we can connect to the contrapositive of P1: not SL ==> not GS ==> not IPC. So, using the transitive property, we can conclude: not SL ==> not IPOC, i.e. answer choice (A).

Hope that helps! Please let us know if you have any other questions.

Saira on January 13, 2015

I thought that premise two will be diagrammed like this
-Not Good Show - > Sophisticated listener

Is this correct ?

Melody on January 14, 2015

Premise two is an "unless" statement. So we negate the part that does not come after the "unless," and regard that as our sufficient condition.

Thus, we negate "not be a good show," which becomes "be a good show."

So our sufficient condition is "be a good show" and our necessary condition is what follows after the "unless," which in this case is: "there are sophisticated listeners."

So we must diagram "P2" like so:

P2: GS ==> SL
not SL ==> not GS

Hope that clears things up! Please let us know if you have any other questions.

Rex on September 25, 2017

Hi Naz. Will you explain why answer choice B is not correct? Will you diagram answer choice B please? Thank you. -Rex

Mehran on September 28, 2017

Hi Rex! Yes, let's diagram answer choice (B).

No people who understand their musical roots will be in the audience

If the audience will not be treated to a good show.

If the audience will not be treated to a good show = sufficient condition = not GS

No people who understand their musical roots will be in audience = necessary condition = no UMR

Put it together:

not GS ==> no UMR

Now, this is a Must Be True question, so the correct answer must be textually supported by the stimulus.

If you combine the contrapositive of the 3rd premise (not UMR ==> not SL) and the contrapositive of the 2nd premise (not SL ==> not GS), then you get not UMR ==> not GS, via the transitive property.

Notice how answer choice (B) has this flipped, incorrectly. This is why answer choice (B) fails the "must be true" test and can be eliminated.

Hope this helps! Please let us know if you have any additional questions.

on October 21, 2017

For key words like unless where one must either negate necessary or the sufficient condition I get confused because I don't see where or how it is that you negate them. I've been dying to ask this question because it really confuses me.

Mehran on October 22, 2017

Hi @rfpo1395, thanks for your post! The easiest way to get comfortable with these rules is to learn them by heart. I recommend keeping a list that you add to as you study.

For unless statements, here is the rule:
1. The necessary condition follows after the "unless," and then
2. Negate the other part of the sentence (the sufficient part)

For example: A unless B is diagrammed
not A ==> B

Hope this helps! Best of luck!

niki on September 29, 2018

Isn't this question a transitive properties question?
IPC --> GS --> SL --> MR
not MR --> not SL --> not GS --> not IPC

Meaning we just use our chain and we can see that in answer A, it says
no SL --> no IPC which follows our link correctly (meaning it doesn't just reverse and it doesn't just negate as per rules).

Chazz on October 18, 2018

Naz states that to come to the conclusion that NotSL==>NotIPC you start with the contrapositive of P2. How do you come to that conclusion? How do you know that's what you do when approaching a question like this? I get everything up until that point.