#18 - Leadership depends as much on making one’s followers

[Administrator]

Complete Question Explanation

Cannot Be True—SN. The correct answer choice is (E)

We are told that if people follow a leader, it is necessary that the be convinced both that their efforts are required to accomplish a goal, and that that goal will actually be accomplished:

• PFL Efforts Nec + Achieve Goal

To prove an answer choice Cannot Be True, show that the sufficient condition has been met (people follow a leader) without the necessary conditions.

Answer choice (A): There is never a connection mentioned between people feeling their efforts are necessary and people achieving a goal. All we know is that these two conditions are necessary for people to follow a leader.

Answer choice (B): The stimulus never talks about actually achieving a goal (only about convincing people that the goal would be achieved), so this is new information and is not impossible based on the stimulus.

Answer choice (C): There could be other circumstances besides being a leader when it would be necessary to convince people that their efforts were required to achieve a goal, so this answer choice is not ruled out by the stimulus.

Answer choice (D): It is entirely possible that people can achieve a goal regardless of whether they believed that achievement could happen, so this answer choice could be true.

Answer choice (E): This is the correct answer choice. As mentioned above, if people follow a leader it must be true that they feel their efforts are necessary. So it cannot be true that they follow a leader without meeting this necessary condition.

[kristinaroz93]

"Leadership depends as much on making one's followers aware of their own importance as it does on conveying a vivid image of a collective goal.."

This is from the set of cannot be true questions in the section.

First question:
Is choice c a mistaken reversal?
effort necc + achieve goal--> people follow leader
If so, what makes the mistaken reversal in this answer choice not cannot be true? Is it because there could just also be other circumstances in which other than being a leader (necc condition in this case) where efforts are necessary (sufficient condition). (In general, will mistaken reversals or even mistaken negations be wrong answers for these conditional reasoning cannot be true questions? Is the strategy for conditional reasoning cannot be true questions then only to seek out answer choices where the sufficient occurs and the necc does not and avoid everything else?)

2nd question:
Can we elminate D on the basis that because achieving a goal is on the right side of the conditional (i.e. it's a necc statement), there is not much we can infer from it?

or is it because choice D is talking about "succeeding in achieving a goal", whereas the stimulus never talks about actually achieving the goal only about convincing people that their efforts are required to do so.

(Essentially how can I elminate choice D, I was a tad bit confused by the online student center explanation of it)

3rd question:
And E is right because: necc condition has to be met for the sufficient to be true (as per my discussion earlier). And here the necc condition is not met, since one has to be convinced 100% that their efforts are needed in attainment of a goal and not be unsure about it, while the sufficient was stated to have occured. Is my reasoning here okay?

Please let me know if I have made some horrid mistakes in my thinking or if I am not making any sense. I apologize for the long post!

Best,

Kristina

[David Boyle]

"Leadership depends as much on making one's followers aware of their own importance as it does on conveying a vivid image of a collective goal.."

This is from the set of cannot be true questions in the section.

First question:
Is choice c a mistaken reversal?
effort necc + achieve goal--> people follow leader
If so, what makes the mistaken reversal in this answer choice not cannot be true? Is it because there could just also be other circumstances in which other than being a leader (necc condition in this case) where efforts are necessary (sufficient condition). (In general, will mistaken reversals or even mistaken negations be wrong answers for these conditional reasoning cannot be true questions? Is the strategy for conditional reasoning cannot be true questions then only to seek out answer choices where the sufficient occurs and the necc does not and avoid everything else?)

2nd question:
Can we elminate D on the basis that because achieving a goal is on the right side of the conditional (i.e. it's a necc statement), there is not much we can infer from it?

or is it because choice D is talking about "succeeding in achieving a goal", whereas the stimulus never talks about actually achieving the goal only about convincing people that their efforts are required to do so.

(Essentially how can I elminate choice D, I was a tad bit confused by the online student center explanation of it)

3rd question:
And E is right because: necc condition has to be met for the sufficient to be true (as per my discussion earlier). And here the necc condition is not met, since one has to be convinced 100% that their efforts are needed in attainment of a goal and not be unsure about it, while the sufficient was stated to have occured. Is my reasoning here okay?

Please let me know if I have made some horrid mistakes in my thinking or if I am not making any sense. I apologize for the long post!

Best,

Kristina

Hello kristinaroz93,

You sure want to understand everything about this question!

First: re "(In general, will mistaken reversals or even mistaken negations be wrong answers for these conditional reasoning cannot be true questions? Is the strategy for conditional reasoning cannot be true questions then only to seek out answer choices where the sufficient occurs and the necc does not and avoid everything else?)", yes, they will likely be wrong answers, since they might be true. E.g., "If I'm happy, I eat ice cream" does not always mean, "If I eat ice cream, I'm happy". Maybe you eat ice cream when you're sad, too. But sometimes, you could have both at once (happy, ice cream), so it's not a "Cannot Be True".

And no, looking for "sufficient-without-its-corresponding-necessary" is not the only strategy for finding the right answer, it's just one of them. There are other ways to be false.
And...yes, answer C looks like a bit of a mistaken reversal.

Second: a big problem with D is that it doesn't talk about leaders. The stimulus links leadership to the stuff about convincing people re goals etc. So without that link to leader issues, practically anything maybe could be possible.

Third: that's basically correct; the necessary is missing, so sufficient can't occur.

Hope this helps,
David

[kristinaroz93]

Dear David,

Your response was very helpful to me, very clear and concise!!

Also, what about mistaken negations, could they possibly be correct in the way mistaken reversals are?

And what are some other strategies you would say (since the books do not really cover this a whole lot- lesson books particularly, haven't gone through the bibles yet) when approaching conditional cannot be true questions?

=D

Best,

Kristina

[Dave Killoran]

Hi Kristina,

Thanks for the questions!

As for your first question, yes, it is also true that Mistaken Reversals are likely to be incorrect answer choices in the same way that Mistaken Negations are. After all, a Mistaken Negation and a Mistaken Reversal are simply different ways of expressing the same idea. the analogy I use when teaching and in the Logical Reasoning Bible is that it's like looking at the two sides of a penny: each side appears different, but underneath the value is the same).

As for other strategies in Cannot Be True questions that feature conditional reasoning, you have to consider what a Cannot question seeks as the correct answer: something that is a clear violation of the situation presented in the stimulus. So, the most basic presentation that is used is something like:

• Simple Conditional Statement:
  
  Stimulus: A B
  
  Correct answer: A and B occur (violates the basic conditional above)

Of course, that presentation is pretty straightforward, and so typically you won't see it in that form. What they will do instead is use a chain of statements or they will use statements with either multiple sufficient conditions, multiple necessary conditions, or both. Those look far more complex than our example above, but often they are based on the same basic error. Here are some examples:

• Compound Sufficient Condition:
  
  G
  Stimulus: + J
  H
  
  Correct answer: G, H and J occur (violates the conditions above)
  
  
  
  Chain:
  
  Stimulus: A B C
  
  Correct answer possibilities:
  
  A and C occur (violates the 1st/3rd terms in the conditional chain above)
  B and C occur (violates the 2nd/3rd terms in the conditional chain above)
  A and B occur (violates the 1st/2nd terms in the conditional chain above)

The statements above are a bit more complex than the initial statement (especially so when we have multiple conditional relationships as in the last example), and then if we added negatives into the stimulus statements, that would make it even more complex. So, they can level up the difficulty of these problems but at the core they still rely on the same basic error.

The thing to focus on in Cannot questions—whether conditional or not—is that there is a black and white certainty to these just as in Must Be True questions. We're just looking at the other end of the truth spectrum in Cannot questions. Because of this, the Fact Test applies, and, as my colleague Clay Cooper points out, this approach means that you focus on the "right" side of the various conditional rules—meaning, the necessary conditions—on the events or terms that can be proved under certain circumstances.

Please let me know if that helps. Thanks!

[kristinaroz93]

Dear David and Dave,

Thank you so much for your swift responses, I am very appreciative of all the help you have provided me! The explanations were very clear and concise. I now know what to look for in these cannot be true conditional questions, which is that regardless of how complex the conditional chain can become, we have to make sure the necc always occurs if the sufficient does! And of course that the statements can be proven false in general in the same way mbt can!

I thank you for all the help!

Best,

Kristina

[dshen123]

Dear staff,
What does E mean? since it triggered the negation of the necessary condition we must negate the sufficient condition for it to be true? that's different from the concept of "failing to ignore that sufficient could occur without meeting the necessary condition", right?
Thank you!

[Jeff Wren]

Hi dshen,

Answer E is stating that there are times in which people will follow a leader even if they have not been convinced (i.e. remain unsure) that their efforts are needed to achieve the collective goal.

This cannot be true based on the stimulus because the stimulus states that anytime people follow a leader, they must be convinced that their efforts are need to achieve the collective goal (according to the stimulus, this is absolutely necessary with no exceptions).

What Answer E is showing is the sufficient condition from the stimulus (people following a leader) without one of the necessary conditions (be convinced that their efforts are need to achieve the collective goal), This violates the conditional statement in the stimulus and therefore cannot be true based on the stimulus.