Given the inequalities: $$L \leq T \leq I \leq M

Question

Given the inequalities:

$$L \leq T \leq I \leq M < X, \quad W < P \leq L \geq B \geq K$$

Determine the truth of the following conclusions:

I. $K \geq M$

II. $P > M$

Choose the correct option based on the conclusions.

Accepted Answer

**Solution:** 1. From the given inequalities: - $L \leq T \leq I \leq M < X$ - $W < P \leq L \geq B \geq K$ 2. Analyze conclusion I: $K \geq M$ - From $L \geq B \geq K$, $K$ is less than or equal to $B$, which is less than or equal to $L$. - From $L \leq T \leq I \leq M$, $L$ is less than or equal to $M$. - Therefore, $K \leq L \leq M$, so $K \geq M$ is **false**. 3. Analyze conclusion II: $P > M$ - From $W < P \leq L \leq M$, since $P \leq L$ and $L \leq M$, it follows that $P \leq M$. - Therefore, $P > M$ is **false**. **Answer:** (c) if neither conclusion I nor II is true.

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