Curioustab Logo Curioustab
Home » Verbal Reasoning » Statement and Conclusion

Examine the statements:\nI. I watch TV only if I am bored. (Watching TV ⇒ Bored)\nII. I am never bored when I have my brother’s company. (Brother’s company ⇒ Not bored)\nIII. Whenever I go to the theatre, I take my brother along. (Theatre ⇒ Brother’s company)\n\nWhich conclusion is valid?

Difficulty: Medium

Correct Answer: If I am not bored, I do not watch TV

Explanation:


Introduction / Context:
We must convert verbal conditionals into logical implications and identify a conclusion that necessarily follows. The key phrase “only if” establishes a necessary condition.


Given Data / Assumptions:

  • I: WatchTV ⇒ Bored (necessary condition = “bored”).
  • II: Brother ⇒ Not bored.
  • III: Theatre ⇒ Brother.


Concept / Approach:
From “P only if Q” we get P ⇒ Q. The valid contrapositive is ¬Q ⇒ ¬P. Hence from I we also obtain: Not bored ⇒ Do not watch TV.


Step-by-Step Solution:

• Option D is the contrapositive of I and is therefore valid: Not bored ⇒ Not watch TV.• Option A (“If bored, watch TV”) is the converse; it does not follow from “only if.”• Option B introduces seeking brother’s company; not implied.• Option C claims absence of brother ⇒ watch TV; not stated.• Option E claims theatre implies boredom; but Theatre ⇒ Brother ⇒ Not bored, which actually blocks TV watching during theatre times.


Verification / Alternative check:
Construct a timeline: During theatre (with brother), not bored; thus by I’s contrapositive, no TV—consistent with D.


Why Other Options Are Wrong:
They confuse converse with contrapositive or add unstated behaviors.


Common Pitfalls:
Misinterpreting “only if,” assuming “if and only if,” or overlooking the contrapositive.


Final Answer:
If I am not bored, I do not watch TV.

← Previous Question Next Question→

More Questions from Statement and Conclusion

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion