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If all students study hard, then they will pass the exam. John is a student and

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Question: If all students study hard, then they will pass the exam. John is a student and he passed the exam. Can we conclude that John studied hard?

Options:

  1. Yes
  2. No
  3. Only if he studied last night
  4. Cannot be determined

Correct Answer: No

Solution: 

The conclusion is not valid because passing the exam does not necessarily mean that John studied hard; he could have passed for other reasons.

If all students study hard, then they will pass the exam. John is a student and

Practice Questions

Q1
If all students study hard, then they will pass the exam. John is a student and he passed the exam. Can we conclude that John studied hard?
  1. Yes
  2. No
  3. Only if he studied last night
  4. Cannot be determined

Questions & Step-by-Step Solutions

If all students study hard, then they will pass the exam. John is a student and he passed the exam. Can we conclude that John studied hard?
  • Step 1: Understand the statement 'If all students study hard, then they will pass the exam.' This means studying hard is a requirement for passing.
  • Step 2: Identify that John is a student and he passed the exam.
  • Step 3: Realize that just because John passed the exam, it does not mean he studied hard. He could have passed for other reasons, like having prior knowledge or help from others.
  • Step 4: Conclude that we cannot definitively say John studied hard just because he passed the exam.
  • Logical Implication – The question tests understanding of logical implications and the difference between necessary and sufficient conditions.
  • Fallacy of Affirming the Consequent – The reasoning in the question exemplifies the fallacy of affirming the consequent, where one incorrectly infers the antecedent from the consequent.
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