Step 1 — Find the direction ratios of the first line.

The line is given by $x = py + q$, $z = ry + s$. Treat $y$ as the parameter and put $y = t$:

$$x = pt + q, \qquad y = t, \qquad z = rt + s$$

Writing this in symmetric form:

$$\frac{x - q}{p} = \frac{y}{1} = \frac{z - s}{r}$$

So $\vec{b_1} = \langle p,\; 1,\; r\rangle$.

Step 2 — Find the direction ratios of the second line.

By exactly the same reasoning,

$$\vec{b_2} = \langle p',\; 1,\; r'\rangle$$

Step 3 — Apply the perpendicularity condition.

$$\vec{b_1}\cdot\vec{b_2} = 0$$

$$pp' + (1)(1) + rr' = 0$$

$$pp' + rr' = -1$$

Step 4 — Compare with the Assertion.

The Assertion claims the condition is $pp' + rr' = 1$, but the correct condition is $pp' + rr' = -1$.

Assertion (A) is FALSE.

Step 5 — Examine the Reason.

Two lines are perpendicular exactly when their direction vectors are perpendicular, i.e. $\vec{b_1}\cdot\vec{b_2} = 0$. This is the standard and correct condition.

Reason (R) is TRUE.

Step 6 — Conclusion.

Assertion is false and Reason is true.

$$\boxed{\text{Option (D)}}$$

Note: the middle direction ratio of each line is $1$ (since $y$ itself is the parameter). Forgetting this "$+1$" is exactly the slip that produces the wrong condition $pp' + rr' = 1$.