**Statement:** V M; W P ≥ X **Conclusions:** I. P Q II. Q ≥ X Choose the correct option: (a) Only conclusion I is true (b) Only conclusion II is true (c) Either conclusion I or conclusion II is true (d) Neither conclusion I nor conclusion II is true (e) Both conclusions I and II are true

Question

**Statement:** V < Q ≤ R; W = R > M; W > P ≥ X

**Conclusions:**

I. P > Q

II. Q ≥ X

Choose the correct option:

(a) Only conclusion I is true

(b) Only conclusion II is true

(c) Either conclusion I or conclusion II is true

(d) Neither conclusion I nor conclusion II is true

(e) Both conclusions I and II are true

Accepted Answer

**Solution:** 1. From the statement, we have the following inequalities: - $V < Q \leq R$ - $W = R > M$ - $W > P \geq X$ 2. Analyze conclusion I: $P > Q$ - Since $W > P$ and $W = R \geq Q$, it implies $P < W = R \geq Q$. - So, $P$ is less than or equal to $Q$ or less than $Q$, but not necessarily greater. - Therefore, conclusion I is **false**. 3. Analyze conclusion II: $Q \geq X$ - Given $P \geq X$ and $W > P$, but no direct comparison between $Q$ and $X$. - Since $Q \leq R = W$ and $W > P \geq X$, $Q$ could be less than, equal to, or greater than $X$. - Hence, conclusion II is **not necessarily true**. 4. Since neither conclusion I nor conclusion II is definitely true, the correct choice is: **Answer:** (d) Neither conclusion I nor conclusion II is true

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