#9 - Most lecturers who are effective teachers are

[Administrator]

Complete Question Explanation

Must Be True—Formal Logic. The correct answer choice is (A)

This is the first formal logic problem of this section. Since the stimulus has no conclusion, one can reasonably expect that the correct answer choice will be an additive inference drawn from these premises. Examining each premise individually will allow for a determination of which inferences can correctly be drawn.

1. “Most lecturers who are effective teachers are eccentric.”

• ET = lecturers who are effective teachers
  ECC = eccentric
  
  ET ECC

Because “most” statements are not universal, they do not have a valid contrapositive. However, this premise does yield the inherent inference that some people who are eccentric are effective teachers (and vice versa), or

• ECC ET

2. “Some noneccentric lecturers are very effective teachers.”

• ECC = noneccentric
  
  ECC ET

Like “most” statements, “some” statements have no logical contrapositive. Also, “some” statements can only be combined with universal relationships to create additive inferences. Thus, there are no additive inferences between the first and second premises of this argument.

3. “Every effective teacher is a good communicator.”

• GC = good communicator
  
  ET GC

This final premise yields a contrapositive (“Those who are not good communicators are not effective teachers”) and can be combined with our existing premises to form additive inferences. For example, one can now conclude that some noneccentric lecturers are good communicators by combining the second and third premises:

• ECC ET GC, therefore: ECC GC

Also, the inherent inference from the first premise can be combined with the third premise in the following manner:

• ECC ET GC, therefore: ECC GC

Since all “some” relationships are inherently reversible, this inference is identical to answer choice (A).

Answer choice (A): This is the correct answer choice. As demonstrated above, the first premise contains an inherent “some” inference (“Some lecturers who are eccentric are effective teachers”). This “some” inference, together with the third premise, leads to the additive inference that “Some lecturers who are eccentric are good communicators.” Reversing this relationship yields “Some good communicators are eccentric.”

Answer choice (B): This is simply a Mistaken Reversal of the third premise. Some good communicators may not be effective teachers, so this answer is incorrect.

Answer choice (C): From the third premise, one can infer that those who are not good communicators will not be effective teachers. However, this inference cannot be combined with any other premise or inference to determine whether or not such people will be eccentric. Thus, this answer is unsupported by the stimulus.

This is a very common incorrect answer choice in “some”-based formal logic questions, as test takers often mistakenly presume that “Some are XYZ” implies that “Some are not XYZ.” In other words, just because it can be determined that some noneccentric lecturers are effective teachers (from the second premise; reversed: some lectures who are effective teachers are not eccentric) does not mean that some noneccentric lecturers are not effective teachers (or vice versa; that some lectures who are not effective teachers are not eccentric).

Answer choice (D): The terms “effective teacher” and “good communicator” are not logically equivalent. Being a good communicator does not necessarily ensure that one will also be an effective teacher. Thus, the latter term (good communicator) cannot correctly be substituted for the former (effective teacher) in the first premise.

Answer choice (E): According to the third premise, it is not possible for someone to be an effective teacher without being a good communicator. Since this answer choice contradicts one of the premises, this inference cannot be correct.

[melissa27]

Can you please go through the diagrams for this stimulus, including how to arrive at the correct answer?

[Jon Denning]

Let's diagram out each of the pieces here, then put them together to find our inference.

First, a rundown of notations: ET (effective teachers), Ecc (eccentric), Comm (good communicator)

I diagrammed the first part of sentence 1 as ET --most--> Ecc [note: I didn't worry about the idea of "lecturers" here since that's more or less implied by "teacher" and doesn't come up again in the stimulus]

Second part of sentence 1: NOT Ecc <--some--> ET

Second sentence: ET --> Comm

With that second sentence we find a shared term, ET. So we can form two combined chains:

Comm <-- ET --most--> Ecc [inference: Comm <--some--> Ecc]

NOT Ecc <--some--> ET --> Comm [inference: NOT Ecc <--some--> Comm]

So our two inferences are essentially "Some good communicators are eccentric," and "some good communicators are noneccentric."

Answer choice A represents the first of those inferences.

B is a mistaken reversal of the last sentence.
C is wrong because we don't have the term NOT ET pointing to anything (hence no inference)
D is a mistake from the first chain above where we cannot connect Comm and Ecc with a Most because the arrows do not go in the same direction (and we'd need the Most arrow to start the chain, which it doesn't)
E is wrong because it says every effective teacher is a good communicator in the second sentence


This is pretty classic Formal Logic, which is covered extensively in an online supplement for our FL and Online students, so I'd encourage you to check that out if you're a student and interested in exploring it further.

Hope that helps!

JD

[Nel]

Hello.

I am struggling with Conditional Reasoning Must Be True problems that involves modifiers, such as "most", "some", "few", "no", etc. Maybe my struggle is caused by double arrow as well.

Below is the specific problems that I do not understand.

1) PRACTICE TEST 2004 JUNE, Section 3, #9


Could anybody explain why the right answers are right?

Here is how I diagrammed.
1) PRACTICE TEST 2004 JUNE, Section 3, #9
Effective Teachers (EFF) Eccentric (ECC)

ECC EFF
　　(some)
EFF Good Communicater (GC)

The answer (MBT) was "Some GC are ECC".

GC is necessary factor, nut sufficient factor.
And the contra positive would be GC EFF
So, I do not understand how this logic would end something like
GC ECC
　(some)

[Lucas Moreau]

The trick to this question is in grouping, to an extent. You know that most EFF teachers are ECC, and that even some not-ECC teachers can also be EFF. And since all EFF teachers are GC, there is a non-zero population of both ECC and not-ECC teachers who are GC. Anything other than zero is enough for "some", and thus, it must be true that some GC are EFF.

Hope this helps,
Lucas Moreau
PowerScore

[eober]

Hi,

Would you be able to let me know if I am correct in my reasoning in this question:

Most effective lecturers eccentric

some (not)eccentric effective

effective good communicator

From here can we combine the first and the third conditionals to say:

most effective good communicator + eccentric

Is this how we end up with answer choice A?


Thank you!

[Lucas Moreau]

Hello, eober,

That is a correct line of reasoning. Well done! If every effective teacher is also a good communicator, and most lecturers who are effective teachers are eccentric, there must be some non-zero number of lecturers who are effective teachers, good communicators, and eccentric all at once.

Good job,
Lucas Moreau

[amna.ali467]

Hi,

What is the set up for the conditional reasoning in this question in order to show that answer choice A is correct?

Thanks!

[Nikki Siclunov]

Hi amna.ali467,

The stimulus can be diagrammed as follows:

Effective lecturers Eccentric

Effective lecturers Non-eccentric

Effective Good communicator

If most effective lecturers are eccentric, it follows that some eccentric people are effective lecturers. But, according to the last sentence, every effective teacher is a good communicator. So, some eccentric people are good communicators (and vice versa).

Thanks!

[ClaudiaK32]

I'm sorry but I still do not understand why D is not correct.