Logical Reasoning

PT101 · S2 · Q11 Not surprisingly, there are no

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Not surprisingly, there are no professors under the age of eighteen.

Statements

conditionals (no / no one)

Professor → 18+ under 18 → ~Professor

under 18 → ~vote legally vote legally → 18+

quantifiers (some)

Some brilliant people are professors Some brilliant people are legal voters Some brilliant people are under 18

Evaluate

Whenever we're given conditional rules, we want to figure out whether they chain together and whether we can apply them to any provided facts.

Do our two conditionals chain together?

No, but they have a common trigger. We could say that, under 18 → Professor and vote legally

Do our conditionals apply to any of the provided facts? (i.e. do the provided facts mention any of the triggers?)

Sure,

Some brilliant people are professors so some brilliant people are 18+

Some brilliant people are legal voters so some brilliant people are 18+

Some brilliant people are under 18 so some brilliant people are not-professors and not legal voters.

Goal

Let's look for an answer rewarding us for making any of these inferences:

- some people are brilliant, professors, and 18+ - some people are brilliant, legal voters, and 18+ - some people are brilliant, under 18, not professors, and not legal voters

11.

If the statements above are true, then on the basis of them which one of the following must also be true?

  1. No professors are eighteen-year-olds.

    Potentially Contradicted

    One of our inferences allows for brilliant, 18-year old professors. - some people are brilliant, professors, and 18+ - some people are brilliant, legal voters, and 18+ - some people are brilliant, under 18, not professors, and not legal voters No professors are under the age of 18, but that doesn't mean no professors are age 18.

    4% picked this

  2. All brilliant people are either

    Too Strong: all

    We can't say anything about all brilliant people, because the passage didn't ever tell us something that was true about all brilliant people. It's possible that there's a brilliant person who isn't a professor, isn't a legal voter (maybe he's a felon or just never registered to vote), and is 18 or older.

    3% picked this

  3. Some legal voters are not

    Unsupported Overlap

    Did we ever derive that "legal voter" and "not professor" were found in the same person? - some people are brilliant, professors, and 18+ - some people are brilliant, legal voters, and 18+ - some people are brilliant, under 18, not professors, and not legal voters Nope. We know that some brilliant people are legal voters and that some brilliant people are not professors, but we don't have any way to prove those are the same people.

    16% picked this

  4. Some professors are neither legal

    Out of Scope: not brilliant

    The passage provided zero information about people who are not brilliant.

    3% picked this

  5. Correct

    Some brilliant people are neither

    Why this is right

    Did we ever derive that "brilliant" and "not professor" and "not voter" were found in the same person? - some people are brilliant, professors, and 18+ - some people are brilliant, legal voters, and 18+ - some people are brilliant, under 18, not professors, and not legal voters Yes, that's our final line. We know some brilliant people are under 18, which proves they are not professors and not legal voters.

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

    74% picked this

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