Directions: In which of the following expressions does the relationship M ≥ R and Q > W definitely hold true, assuming the given statements are true?

The correct option in which both the relationships $M\ge R$ and $Q>W$ definitely hold true is P < R ≤ W > S; M ≥ W < Y ≤ Q.

To verify why both conclusions hold true, let us break down the logical reasoning step-by-step:

Step 1: Check the relationship between M and R

From the first statement, we have:

$R\le ;W$

This is logically equivalent to saying:

$W\ge R$

From the second statement, we have:

$M\ge W$

Combining $M\ge W$ and $W\ge R$ through the common variable $W$ gives:

$M\ge W\ge R$

Since the inequality signs point in the same direction without any contradiction, we conclude that:

$M\ge R$

Hence, the relationship $M\ge R$ definitely holds true.

Step 2: Check the relationship between Q and W

From the second statement, looking at the path connecting $W$, $Y$, and $Q$:

$W<Y\le ;Q$

Since $W$ is strictly less than $Y$ ($W<Y$), and $Y$ is less than or equal to $Q$ ($Y\le ;Q$), the relationship between $W$ and $Q$ is strictly:

$W<Q$

Reversing $W<Q$ gives:

$Q>W$

Hence, the relationship $Q>W$ also definitely holds true.

Therefore, the expression P < R ≤ W > S; M ≥ W < Y ≤ Q satisfies both required conditions.