Examine the statements: I. I watch TV only if I am bored. (Watching TV ⇒ Bored) II. I am never bored when I have my brother’s company. (Brother’s company ⇒ Not bored) III. Whenever I go to the theatre, I take my brother along. (Theatre ⇒ Brother’s.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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.

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

More Questions from Statement and Conclusion

Discussion & Comments