Logical Reasoning

PT122 · S2 · Q16 Most successful entrepreneurs work at least

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Most successful entrepreneurs work at least 18 hours a day, and no one who works at least 18 hours a day has time for leisure activities.

Statements

Quantifiers / Conditionals (most, no, all)

Any time we have a mix of quantified claims and conditionals, we want to prioritize conditionals.

Happy → Time for entrepreneur Leisure

Work at → No time for least 18hrs Leisure

These both have the concept of "time for leisure", so we should see whether they chain together. If we contrapose either one, we can chain them together.

Happy → Time for → Work less than entrepreneur Leisure 18 hrs / day

Then we get our Most claim.

Most successful are Work at least entrepreneurs 18 hrs / day

The overlapping term is whether you work at least 18 hrs. We'll have to contrapose our chain so that it's starting from "Work at least 18".

Work at → No time for → Not happy least 18hrs Leisure entrepreneurs

Evaluate

So since we know that , we know the other two ideas on this chain as well:

Most successful entrepreneurs have not time for leisure. Most successful entrepreneurs are not happy.

Goal

The correct answer to Must Be False almost always either contradicts a conditional relationship we're given or contradicts an inference we can derive.

So we might see our inferences contradicted: - Most successful do have leisure time - Most successful are happy

Or we'll see our conditional chain contradicted: - Someone works at least 18, but is happy. (for example)

16.

If the statements above are true, each of the following could be true EXCEPT:

  1. Anyone who has no time

    Compatible

    This goes from the 2nd idea backwards to the 1st idea. Work at → No time for → Not happy least 18hrs Leisure entrepreneurs That's not a legal inference, but it's not contradicting this chain. To contradict a conditional, you need a case where "Left side is true, Right side is false".

    18% picked this

  2. Some entrepreneurs who work at

    Compatible

    This doesn't contradict our conditional chain (because successful isn't even part of that). Work at → No time for → Not happy least 18hrs Leisure entrepreneurs And it doesn't contradict either of our Most inferences: - Most Successful have no leisure time - Most Successful are not happy

    2% picked this

  3. Some happy entrepreneurs are successful.

    Compatible

    This doesn't contradict our conditional chain (because successful isn't even part of that). Work at → No time for → Not happy least 18hrs Leisure entrepreneurs And it doesn't contradict either of our Most inferences: - Most Successful have no leisure time - Most Successful are not happy

    9% picked this

  4. Correct

    Some entrepreneurs who work at

    Why this is right

    This contradicts our conditional chain. Work at → No time for → Not happy least 18hrs Leisure entrepreneurs The left side is true (they work at least 18), and the right side is false (they are happy).

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

    68% picked this

  5. Some successful entrepreneurs work less

    Compatible

    This doesn't contradict our conditional chain (because successful isn't even part of that). Work at → No time for → Not happy least 18hrs Leisure entrepreneurs And it doesn't contradict either of our Most inferences: - Most Successful have no leisure time - Most Successful are not happy

    3% picked this

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