Hard
counterexampleslogical-fallaciesaffirming-consequent

Which Example Shows That the Argument Is Invalid?

Problem Statement

Argument: 'All successful people wake up early. Therefore, if you wake up early, you will be successful.' Which counterexample shows this argument is invalid? A) A successful person who wakes up late. B) An unsuccessful person who wakes up early. C) A successful person who wakes up early. D) An unsuccessful person who wakes up late.

Answer

B) An unsuccessful person who wakes up early

Step-by-Step Explanation

  1. 1

    The argument commits the 'affirming the consequent' fallacy.

  2. 2

    Original: All successful people wake up early (Success → Early)

  3. 3

    Claimed: Waking up early → Success

  4. 4

    This reverses the logic incorrectly.

  5. 5

    To show it's invalid, we need a counterexample where someone wakes up early but isn't successful.

  6. 6

    Option A: Successful + late waking — contradicts the premise, not the conclusion.

  7. 7

    Option B: Unsuccessful + early waking — PERFECT. Shows waking up early doesn't guarantee success.

  8. 8

    Option C: Successful + early waking — supports the premise, doesn't refute the conclusion.

  9. 9

    Option D: Unsuccessful + late waking — consistent with both statements, not a counterexample.

  10. 10

    Option B is the counterexample that invalidates the argument.