Given the statements: $P M \geq I W$ Determine which of the following conclusions are definitely true: I. $S \leq M$ II. $Z W$

Question

Given the statements:

$P > M \geq I < Z$; $S \leq I = K > W$

Determine which of the following conclusions are definitely true:

I. $S \leq M$

II. $Z > W$

Accepted Answer

**Solution:** 1. Analyze the given statements: - $P > M \geq I < Z$ - $S \leq I = K > W$ 2. From $P > M \geq I$, we know $M \geq I$ and $P > M$. 3. From $S \leq I = K$, it follows that $S \leq I$ and $I = K$. 4. Since $I < Z$, it means $Z$ is greater than $I$. 5. Also, $K > W$ and since $I = K$, it implies $I > W$. 6. Now, check conclusion I: $S \leq M$. - Given $S \leq I$ and $M \geq I$, so $S \leq I \leq M$. - Therefore, $S \leq M$ is true. 7. Check conclusion II: $Z > W$. - From above, $Z > I$ and $I > W$. - By transitive property, $Z > W$ is true. **Answer:** Both conclusions I and II are true, so option (e) is correct.

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