Logical Reasoning

PT116 · S3 · Q9 Most lecturers who are effective

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Most lecturers who are effective teachers are eccentric, but some noneccentric lecturers are very effective teachers.

Statements

Quantifiers (most, some)

people who are Most lecturers and are eccentric effect. teachers

Some noneccentric are very lecturers effective

Conditional (every)

Effective → Good teacher Communicator

Evaluate

Whenever we see quantifiers like most / some / all, we want to see if there are two Most facts about the same group. If we know , we can infer "Some B's are C".

But there's only one most fact here.

Whenever we see conditionals, we ask ourselves 1. does this chain up to any other conditional? 2. can I apply this rule (or its contrapositive) to any of the other facts provided?

There's only one conditional, so there won't be a conditional chain. Can we apply this rule to any facts? Were we told about any effective teachers?

Yes, we heard about lecturers who are also effective teachers. Most of them are eccentric. And since all of them by definition are effective teachers, we know that all of them are good communicators.

That would allow us to derive a Trait Overlap inference: there are people who are both eccentric and good communicators.

We're also told that some noneccentric lecturers are very effective teachers, so according to this conditional rule they are also good communicators.

Thus we can also derive the Trait Overlap that some people are both noneccentric and good communicators.

Goal

It seems like the Trait Overlap inferences are the most likely options for the correct answers, so look for a safely worded answer that acknowledges that "eccentric/noneccentric" and "good communicator" overlap.

9.

Which one of the following statements follows logically from the statements above?

  1. Correct

    Some good communicators are eccentric.

    Why this is right

    The people in the first sentence are lecturers, effective teachers, and eccentric. We're told that every effective teacher is a good communicator. So the people in the first sentence are lecturers, effective teachers, good communicators, and eccentric. That proves that some people are both eccentric and good communicators. More formally, we combine these two Some eccentric are effect teach effect ? good teach comm. and get this inference, Some eccentric are good comm.

    Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.

    66% picked this

  2. All good communicators are effective

    Too Strong: all Illegal Reversal

    We can't say anything about all good communicators, because we were never told anything about that all good communicators. We know that some good communicators are effective teachers. The last sentence says this: effective teacher ? good comm. and this answer illegally reverses that: good comm ? effective teacher

    4% picked this

  3. Some lecturers who are not

    Out of Scope: not effective

    We only heard about teachers who are effective, so we have no information to support any inference about teachers are not effective.

    9% picked this

  4. Most lecturers who are good

    Too Strong: most Unknown Most Group

    This answer talks about most [people who are lecturers and good communicators]. We never got a most fact about that group, so we can't make a most inference about that group. We only got a most fact about the group of [people who are lecturers and effective teachers]. People might be tempted to think, "Can't I just swap out effective with good communicator?" Anywhere we see "effective" we can add "good communicator", but we can't replace it and still be talking about the same group of people. Consider this example: "Most adults who are NFL players are paid over $1 million / year" "Every NFL player is a man." Could we just swap out "NFL player" for "man" and say, "Most adults who are men are paid over $1 million / year"? Of course not. We know that most adult males don't get paid that much. By changing from "most adults who are NFL players" to "most adults who are men" we went from talking about over 50% of a group of about 1000 people (NFL players) to talking about over 50% of a group of about 2 billion people (adult males).

    16% picked this

  5. Some noneccentric lecturers are effective

    Out of Scope: not good communicator

    We only received information about people who are good communicators, so we have no information to support any inference about people who are not good communicators.

    5% picked this

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