Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):

Assertion (A): $\bar{p}$

Reason (R): $(r\to \bar{q},\ r\lor s,\ s\to \bar{q},\ p\to q)$

In the light of the above statements, choose the correct answer from the options given below:

Given Reason statements are:

$r\to \bar{q}$

$r\lor s$

$s\to \bar{q}$

$p\to q$

From $r\lor s$, either $r$ is true or $s$ is true.

Case 1:

If $r$ is true, then using $r\to \bar{q}$, we get:

$\bar{q}$

Case 2:

If $s$ is true, then using $s\to \bar{q}$, we get:

$\bar{q}$

So, in both cases:

$\bar{q}$ is true.

Now we also have:

$p\to q$

Using modus tollens:

$p\to q$ and $\bar{q}$ imply $\bar{p}$.

Therefore, Assertion (A), that is $\bar{p}$, is true.

Also, Reason (R) correctly explains how $\bar{p}$ is obtained.

Hence, both (A) and (R) are true and (R) is the correct explanation of (A).