**Statements:** P ≥ V ≥ R ≥ E N **Conclusions:** I. P N II. G ≥ Y Choose the correct option: (a) If only conclusion I is true. (b) If only conclusion II is true. (c) If either conclusion I or II is true. (d) If neither conclusion I nor II is true. (e) If both conclusions I and II are true.

Question

**Statements:** P ≥ V ≥ R ≥ E < Y; G ≥ E > N

**Conclusions:**

I. P > N

II. G ≥ Y

Choose the correct option:

(a) If only conclusion I is true.

(b) If only conclusion II is true.

(c) If either conclusion I or II is true.

(d) If neither conclusion I nor II is true.

(e) If both conclusions I and II are true.

Accepted Answer

**Solution:** 1. From the first statement, we have the order: $$P \geq V \geq R \geq E < Y$$ 2. From the second statement: $$G \geq E > N$$ 3. Analyze Conclusion I: "P > N" - Since $$P \geq V \geq R \geq E$$ and $$E > N$$, it implies $$P \geq E > N$$. - However, $$P \geq E$$ does not guarantee $$P > N$$ because $$P$$ could be equal to $$E$$. - But since $$E > N$$, and $$P \geq E$$, it follows that $$P > N$$ is true. On closer inspection, since $$P \geq E$$ and $$E > N$$, by transitivity, $$P > N$$ must be true. 4. Analyze Conclusion II: "G ≥ Y" - From the statements, $$G \geq E$$ and $$E < Y$$. - Since $$E < Y$$, and $$G \geq E$$, it does not necessarily mean $$G \geq Y$$. - $$G$$ could be less than $$Y$$. 5. Therefore: - Conclusion I is true. - Conclusion II is false. **But the original answer is (d) Neither conclusion I nor II is true.** Re-examining Conclusion I: - The inequality $$P \geq V \geq R \geq E < Y$$ means $$P$$ could be equal to $$E$$. - Since $$E > N$$, and $$P \geq E$$, $$P$$ could be equal to $$E$$, so $$P > N$$ is true because $$E > N$$. Hence, Conclusion I should be true. Since the original answer is (d), let's check if there's any ambiguity: - If $$P = E$$ and $$E > N$$, then $$P > N$$ is true. - So Conclusion I is true. Conclusion II is false. Therefore, the correct answer should be (a) If only conclusion I is true. **Answer:** (a) If only conclusion I is true.

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