Directions: Treat the statements below as true and identify the conclusion(s) that must follow.

Statements:

$P\ge Q>R,S<T\le Q,R>L$

Conclusions:

I. $P>R$

II. $Q>L$

III. $S<R$

The correct option is Both conclusions I and II are true.

To determine which conclusions logically follow, let us analyze the given statements step-by-step.

Given Statements:

$P\ge Q>R$

$S<T\le Q$

$R>L$

Evaluating Conclusion I:

$P>R$

From the first statement, we are given:

$P\ge Q>R$

Since $P$ is greater than or equal to $Q$, and $Q$ is strictly greater than $R$, combining these inequalities tells us that $P$ must be strictly greater than $R$.

$P>R$

Therefore, Conclusion I is true.

Evaluating Conclusion II:

$Q>L$

From the first statement, we know that $Q>R$, and from the third statement, we know that $R>L$. Combining these two statements gives:

$Q>R>L$

By the transitive property of inequalities, if $Q$ is greater than $R$ and $R$ is greater than $L$, then $Q$ is strictly greater than $L$.

$Q>L$

Therefore, Conclusion II is true.

Evaluating Conclusion III:

$S<R$

From the second statement, we have $S<T\le Q$, which implies:

$S<Q$

From the first statement, we also know that:

$R<Q$

Since both $S$ and $R$ are strictly smaller than $Q$, there is no direct inequality or linkage provided to compare $S$ and $R$ directly. Therefore, no definite relationship can be established between them.

Thus, Conclusion III does not necessarily follow.

Final Summary:

Conclusions I and II are definitely true, while Conclusion III is not. Hence, the correct answer is Both conclusions I and II are true.