Logical Reasoning

PT109 · S3 · Q23 Maria won this year’s local

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Maria won this year’s local sailboat race by beating Sue, the winner in each of the four previous years.

Conclusion (We Can Conclude)

Maria trained hard.

Evidence

Maria won this year's local sailboat race, beating Sue, the winner in each of the four previous years.

Evaluate

We are trying to prove that Maria "trained hard". Did the evidence provide a proving mechanism for that language, i.e. a rule that says "If xyz, then trained hard"?

No, so the correct answer must provide a rule that puts "trained hard" on the right side of the arrow.

What do we know about Maria? - she won this year's local sailboat race - she beat Sue

Goal

The correct answer will give us a rule that we know applies to Maria and that outputs the language that she "trained hard".

So it could be or "If beat Sue, then trained hard"

23.

The conclusion follows logically if which one of the following is assumed?

  1. Sue did not train as

    Unrelated To Goal

    We need a rule that proves that Maria "trained hard", but this is a comparative idea in Relative language. This proves that "Maria trained harder than Sue did", but that doesn't prove she trained hard. Bill Gates is poorer than Jeff Bezos, but that doesn't mean that Bill Gates is poor.

    6% picked this

  2. If Maria trained hard, she

    Illegal Reversal

    We need a rule that proves that Maria "trained hard", so that concept has to be on the right of the arrow. Since this has "trained hard" on the left (the if signifies the sufficient, left-side idea), it's useless to us. If we had a rule that said, "If Maria won the sailboat race, then she trained hard", that would take what we know and output the conclusion we're trying to prove. But this answer is an illegal reversal of that.

    15% picked this

  3. Correct

    Maria could beat a four-time

    Why this is right

    We need a rule that proves that Maria "trained hard", so that concept has to be on the right of the arrow. Since this has "trained hard" on the left (the only if signifies the necessary, right-side idea), it's worth looking at. It says this: if beat a four ? trained hard time winner Is the trigger idea applicable to Maria? Did she beat a four-time winner? Yes, she beat Sue, who won the four previous years. According to this rule, that means that Maria trained hard. So we proved the conclusion! (If you're beating yourself up, thinking, "How were we supposed to know to use the four-time winner part of the premise?", we weren't supposed to know. We're supposed to stay flexible with what the correct answer puts on the left hand side. We can't always predict the trigger language. We just ask ourselves whether the trigger is applicable to the thing we're talking about in the conclusion -- in this case, Maria. We are not flexible when it comes to the right side, though. We have to prove "trained hard", so the right side needs to be saying that or something definitionally equivalent.)

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

    74% picked this

  4. If Sue trained hard, she

    Unrelated To Goal

    We're trying to prove that Maria trained hard, and this is a rule that solely applies to Sue, so it's useless to our purposes.

    3% picked this

  5. Sue is usually a faster

    Unrelated To Goal

    We need a rule that proves that Maria "trained hard", so that concept has to be on the right of the arrow. Since this answer doesn't even deal with the concept of "trained hard", it's useless to us.

    3% picked this

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