STATEMENT-1 : For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary. STATEMENT-2 : If the observer and the object are moving at velocities $v_1$ and $v_2$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $v_2 - v_1$.

Step 1: Analyze Statement-2.

The relative velocity of an object with respect to an observer is defined by the vector difference of their velocities in a common reference frame.

$$\vec{v}_{\text{rel}} = \vec{v}_2 - \vec{v}_1$$

This is a standard definition and is always true. Thus, Statement-2 is true.

Step 2: Analyze Statement-1.

For stationary objects on the ground, their velocity in the laboratory frame is $\vec{v}_2 = 0$, meaning their relative velocity with respect to the train is constant.

$$\vec{v}_{\text{rel}} = -\vec{v}_1$$

The apparent motion perceived by the observer is determined by the angular velocity $\omega$, which is the rate of change of the line-of-sight angle $\theta$.

$$\omega = \frac{d\theta}{dt} \approx \frac{v_1}{D}$$

For nearby objects, the distance $D$ is small, resulting in a large angular velocity $\omega$, so they appear to move rapidly backward.

For distant objects, the distance $D$ is very large, making $\omega \to 0$, so they appear stationary. Thus, Statement-1 is true.

Step 3: Evaluate the relationship between the statements.

The relative velocity is the same for both near and distant objects and does not depend on distance.

$$\vec{v}_{\text{rel}} = -\vec{v}_1$$

Since the explanation for Statement-1 relies on the distance-dependent angular velocity $\omega \approx \frac{v_1}{D}$, Statement-2 is not the correct explanation for Statement-1.

Answer: Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.