Crossroads, a wellness centre allows a member to spend a maximum of one hour in a meditation hall. Shailaja has been in a meditation hall for at least one and a half hours.
Which of the following is a valid conclusion if only the above information is used?
Explanation
To determine the valid conclusion, we must represent the scenario using logical propositions.
Step 1: Formalize the Premises
We know that Crossroads allows a maximum of 1 hour, and Shailaja has spent at least 1.5 hours there. Therefore, if she is at Crossroads, she is necessarily violating the rule:
C⟹V
Step 2: Evaluate the Conclusion
A logical statement is valid if it is the contrapositive of the original conditional statement. The contrapositive of C⟹V is:
¬V⟹¬C
Translating this back into natural language:
Conclusion Analysis:
Option 4 states: "If Shailaja is not violating the wellness centre rule, she is not meditating at Crossroads." This matches the contrapositive logic derived above (¬V⟹¬C).
Options 1, 2, and 3 introduce assumptions or external factors not supported by the strict logical premises provided in the question.
Correct Answer:
The valid conclusion is Option 4.