Logical Reasoning

PT133 · S1 · Q21 On the Discount Phoneline

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On the Discount Phoneline, any domestic long-distance call starting between 9 A.M. and 5 P.M. costs 15 cents a minute, and any other domestic long-distance call costs 10 cents a minute.

Conclusion

Domestic + long distance → costs 15 cents + doesn't cost 10 cents

Evidence

Domestic + long distance → costs 15 cents + 9am - 5pm

Domestic + long distance → costs 10 cents + 5pm - 9am

Evaluation

This argument is valid, since we basically know that domestic long distance calls in two rates: 10 cents and 15 cents. So the conclusion makes sense -- if it ain't 10 cents, it must be 15 cents.

If we were trying to diagram this original argument, we basically need to be convinced that a certain thing (domestic long distance calls) is always going to either be X or Y. Then we can conclude that if it's not X, it's Y.

Goal

Premise 1: If X is A, then it's Y. Premise 2: If X is ~A, then it's Z. Conclusion: If X is ~Y, then it's Z.

21.

The pattern of reasoning in which one of the following arguments is most similar to that in the argument above?

  1. If a university class involves

    Bad Conclusion Match

    The premises do establish that every class that involves lots of lab work will either be lab or normal classroom. A correct conclusion would have said "if a class with lots of lab work isn't lab, then it must be normal classroom" (or vice versa for lab/classroom) But instead, this conclusion is saying "if a class isn't one with lots of lab work". That would only match the original conclusion if the original had said "if a call that isn't domestic long distance doesn't cost 10 cents ..."

    3% picked this

  2. If a university class involves

    Bad Conclusion Match

    The premises do establish that every class that involves lots of lab work will either be lab or normal classroom. A correct conclusion would have said "if a class with lots of lab work isn't lab, then it must be normal classroom" (or vice versa for lab/classroom) But this conclusion doesn't mention the "extensive lab work". This would only match the original conclusion if the original had just said "So if any call doesn't cost 10 cents ...", but it was "So any domestic long-distance call that doesn't cost 10 cents".

    11% picked this

  3. If a university class involves

    Bad Conclusion Match

    This has the same problem as (B). The premises do establish that every class that involves lots of lab work will either be lab or normal classroom. A correct conclusion would have said "if a class with lots of lab work isn't lab, then it must be normal classroom" (or vice versa for lab/classroom) But this conclusion doesn't mention the "extensive lab work".

    6% picked this

  4. If a university class involves

    Bad Conclusion Match

    The premises do establish that every class that involves lots of lab work will either be lab or normal classroom. A correct conclusion would have said "if a class with lots of lab work isn't lab, then it must be normal classroom" (or vice versa for lab/classroom) But this conclusion says "If a class with lots of lab work, then not classroom." That would have been like if the original argument had said "If it's a domestic long-distance call, then it's not 10 cents" (or not 15 cents, same difference)

    4% picked this

  5. Correct

    If a university class involves

    Why this is right

    The premises establish that every class that involves lots of lab work will either be lab or normal classroom. Then the conclusion says, "so if a class with lots of lab work isn't X, then it must be Y".

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

    75% picked this

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