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If all students study hard, then they will pass. John is a student who did not p

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Question: If all students study hard, then they will pass. John is a student who did not pass. Can we conclude that John did not study hard?

Options:

  1. Yes
  2. No
  3. Only if he is not a diligent student
  4. Cannot be determined

Correct Answer: Yes

Solution: 

The conclusion is valid because if all students who study hard pass, then not passing implies John did not study hard.

If all students study hard, then they will pass. John is a student who did not p

Practice Questions

Q1
If all students study hard, then they will pass. John is a student who did not pass. Can we conclude that John did not study hard?
  1. Yes
  2. No
  3. Only if he is not a diligent student
  4. Cannot be determined

Questions & Step-by-Step Solutions

If all students study hard, then they will pass. John is a student who did not pass. Can we conclude that John did not study hard?
  • Logical Implication – Understanding the relationship between premises and conclusions in logical statements.
  • Contrapositive Reasoning – Recognizing that the negation of the conclusion can lead to the negation of the premise.
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