To compare the areas of $\(\triangle P A Q\)$ and $\(\triangle R B S\)$, let's use the properties of parallelograms and triangles.

1. Understand the Parallelogram Properties:

- In a parallelogram PQRS , opposite sides are parallel and equal in length. So, $\(P Q \| S R\)$ and $\(P Q=S R\)$.
- The distance between the parallel lines PQ and SR is the height of the parallelogram. Let's call this height $h$.

2. Understand the Line Segment MN:

- $M$ is the midpoint of $P S$, and $N$ is the midpoint of $Q R$.
- Since M and N are midpoints of opposite sides in a parallelogram, the line segment MN is parallel to PQ and $\(\mathrm{SR}(M N\|P Q\| S R)\)$.
- Furthermore, the line segment MN is exactly halfway between PQ and SR . This means the perpendicular distance from any point on MN to PQ is $h / 2$, and the perpendicular distance from any point on MN to SR is also $h / 2$.

3. Calculate the Area of $\triangle P A Q$ (Quantity A):

- Consider PQ as the base of $\triangle P A Q$. The length of the base is $P Q$.
- The vertex A lies on the line segment MN .
- The height of $\(\triangle P A Q\)$ with respect to base PQ is the perpendicular distance from point A to the line containing PQ .
- Since A is on MN , and MN is parallel to PQ , this perpendicular distance is constant and equal to $h / 2$.
- Area of $\(\triangle P A Q=\frac{1}{2} \times\)$ base $\(\times\)$ height $\(=\frac{1}{2} \times P Q \times \frac{h}{2}=\frac{P Q \times h}{4}\)$.

4. Calculate the Area of $\triangle R B S$ (Quantity B):

- Consider RS as the base of $\(\triangle R B S\)$. The length of the base is $R S$.
- The vertex B lies on the line segment MN .
- The height of $\(\triangle R B S\)$ with respect to base RS is the perpendicular distance from point B to the line containing RS .
- Since B is on MN , and MN is parallel to RS , this perpendicular distance is constant and equal to $h / 2$.
- Area of $\(\triangle R B S=\frac{1}{2} \times\)$ base $\(\times\)$ height $\(=\frac{1}{2} \times R S \times \frac{h}{2}=\frac{R S \times h}{4}\)$.

5. Compare Quantity A and Quantity B:
- We know that $P Q=R S$ because they are opposite sides of a parallelogram.
- Therefore, Area of $\(\triangle P A Q=\frac{P Q \times h}{4}\)$ and Area of $\(\triangle R B S=\frac{P Q \times h}{4}\)$.

Since both expressions are identical, the areas are equal. The specific positions of $A$ and $B$ on the line segment MN do not affect the heights of the triangles relative to their respective bases.

The final answer is The two quantities are equal.