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

Question

Given the inequalities:

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

Determine which of the following conclusions are true:

I. $K < X$

II. $W > M$

Choose the correct option:

Accepted Answer

**Solution:** 1. Given inequalities: - $L \leq T \leq I < M < X$ - $W < P \leq L \geq B \geq K$ 2. Analyze conclusion I: $K < X$ - From the second chain, $K \leq B \leq L$ (since $L \geq B \geq K$) - From the first chain, $L \leq T \leq I < M < X$ - However, the relation between $K$ and $X$ is not directly established because $K$ is only known to be less than or equal to $L$, but $L$ is less than or equal to $T$, etc. - Since $K$ could be equal to $L$ and $L$ could be less than $X$, but $K$ could also be equal to $L$ which might be less than $X$, but no strict inequality $K < X$ is guaranteed. - Therefore, conclusion I is **not necessarily true**. 3. Analyze conclusion II: $W > M$ - From the inequalities, $W < P \leq L \leq T \leq I < M$ - So $W$ is less than $P$, which is less than or equal to $L$, and $L$ is less than or equal to $T$, and so on, all less than $M$. - Hence, $W$ is definitely less than $M$, so $W > M$ is **false**. 4. Since both conclusions I and II are false, the correct choice is (c) neither conclusion I nor II is true. **Answer:** (c)

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