Logical Reasoning

PT11 · S4 · Q22 Paulsville and Longtown cannot both be

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Paulsville and Longtown cannot both be included in the candidate’s itinerary of campaign stops.

Conclusion (clearly, then)

A stop in Longtown can be ruled out.

Evidence

If Salisbury isn't part of the itinerary, then Paulsville will be.

Salisbury is out of the question.

Paulsville and Longtown can't both be included in the itinerary of campaign stops.

Evaluate

This seems like correct logic. We get a conditional saying, ~S → P

We get a fact saying S won't happen. ~S.

That implies that P will happen. And then we have a rule saying that P and L can't both happen. We could write that as a conditional if we wanted. P → ~L L → ~P

Since we know P will happen, that convinces us that L will not happen.

Goal

We need three premises: two conditionals and one fact. One of the conditionals might sound more like a statement of mutual exclusivity (like P and L cannot both be included). The conclusion should be a statement of fact that deals with one of the ideas from the mutually-exclusive conditional.

This is the way the argument worked.

P1: ~X → Y P2: ~X. P3: Y → ~Z C: ~Z.

22.

The reasoning in the argument above most closely parallels that in which one of the following arguments?

  1. The chef never has both

    Bad Evidence Match

    We have our mutually exclusive premise (R and GP are mutually exclusive). And we are concluding that one of those won't happen. And we have a fact triggering a conditional: We have the conditional R → S And the fact "no spinach" triggers the contrapositive and gives us "no radishes". But if there aren't radishes then there could be green peppers. We would need the logic to be telling us there definitely will be radishes so that we could fairly conclude there won't be green peppers.

    27% picked this

  2. Correct

    Tom will definitely support Parker

    Why this is right

    Prem 1: ~X → Y If M doesn't apply, T will support P. Prem 2: ~X. M will not apply. (this implies that T will support P) Prem 3: Y → ~Z T will not support both P and C, so "if T will support P, then T will not support C". Conc: ~Z. T will not support C More conversationally, we have a fact that triggers a conditional: since M will not apply, we know that T will support P. And then we have a mutually exclusive idea: you can't support P and C at the same time. So we get our conclusion. Since T will support P, T will not support C.

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

    59% picked this

  3. The program committee never selects

    Bad Conclusion Match

    The mutually exclusive premise here is that we'll never have two plays by Shaw selected. So the conclusion should be talking about "not selecting a 2nd Shaw play". Instead, it's talking about not selecting a play by Coward. That would be a quick bird's eye view way to eliminate this. If we dug in more to the details, we would see there is a fact that triggers a conditional: Since the committee selected a play by Shaw, they will not select a play by Coward. Thus, the conclusion is valid, but it doesn't come from using a mutually-exclusive premise. It comes immediately as the outcome of one conditional. ORIGINAL THIS ARGUMENT P1: ~X → Y P1: ~X → Y P2: ~X. P2: ~X. P3: Y → ~Z C: Y. C: ~Z.

    9% picked this

  4. In agricultural pest control, either

    Bad Conclusion Match

    As soon as we see that this conclusion is a conditional statement, we can stop reading. The original conclusion was a statement of fact.

    3% picked this

  5. The city cannot afford to

    Bad Evidence Match

    This is like (C). We get a valid conclusion, but it doesn't come from the same combination of logic as the original. There isn't a fact that triggers a conditional. The fact that "the city will only do worthwhile projects" combines with the claim "neither project is worth doing without the other" to give us the inference that "the city will not undertake just one of those projects. It would have to be both or neither." And then that interacts with the claim that "they can't do both" to allow us to infer that "the city will do neither". So it's valid to say that the city won't build the stadium, but it would also be valid to say that the city won't built the new road. That's not like the original argument. The conclusion was "we won't stop in Longtown", but we couldn't have just as easily concluded "we won't stop in Paulsville". The fact that the city won't do either project without doing the other is the opposite of "mutually exclusive" ... it's the idea of "mutually dependent".

    2% picked this

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