Statements:\nA) No teacher comes to the school on a bicycle.\nB) Anand comes to the school on a bicycle.\nConclusions:\nI) Anand is not a teacher.\nII) Anand is a student.

Difficulty: Easy

Correct Answer: Conclusion I alone can be drawn

Explanation:


Introduction / Context:
This is a classic categorical reasoning problem involving a universal negative and a particular instance. We test which conclusions necessarily follow from the premises without importing extra labels (like “student”).


Given Data / Assumptions:

  • Premise A: No teacher uses a bicycle to come to school (Teachers ⇒ not bicycle-users).
  • Premise B: Anand comes to school by bicycle (Anand is a bicycle-user).


Concept / Approach:
From “No teacher is a bicycle-user” and “Anand is a bicycle-user,” we can infer “Anand is not a teacher” (valid by contrapositive / set exclusion). However, nothing is said about Anand’s other possible roles (student, staff, visitor, etc.).


Step-by-Step Solution:
1) Using A and B: If all Teachers ⊆ (not BicycleUsers), then any BicycleUser ∉ Teachers. Since Anand ∈ BicycleUsers, Anand ∉ Teachers ⇒ Conclusion I follows.2) Conclusion II (“Anand is a student”) adds a category never mentioned in the premises. It does not follow.


Verification / Alternative check:
A simple Venn diagram confirms: Anand lies in BicycleUsers; Teachers is a disjoint set from BicycleUsers. Membership in “Student” is undecidable.


Why Other Options Are Wrong:
“Both” and “II alone” overreach; “both cannot” ignores the valid exclusion inference for I.


Common Pitfalls:
Assuming a school-goer riding a bicycle must be a student. The premises do not justify that leap.


Final Answer:
Conclusion I alone can be drawn.

More Questions from Statement and Conclusion

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