Assertion (A) : $\dfrac{1}{2} + 2 = \dfrac{5}{2}$, which is a rational number.

Reason (R) : If $\dfrac{p}{q} \text{ and } \dfrac{r}{s}$ are any two rational numbers then $\dfrac{p}{q} + \dfrac{r}{s} = \dfrac{r}{s} + \dfrac{p}{q}$.

1. Both A and R are correct, and R is the correct explanation for A.

2. Both A and R are correct, and R is not the correct explanation for A.

3. A is true, but R is false.

4. A is false, but R is true.

According to Assertion:

$\Rightarrow \dfrac{1}{2} + 2 \\[1em] \Rightarrow \dfrac{1}{2} + \dfrac{4}{2} \\[1em] \Rightarrow \dfrac{1 + 4}{2} \\[1em] \Rightarrow \dfrac{5}{2}$

A number is rational if it can be written in the form $\dfrac{p}{q}$, where p and q are integers.

Since, $\dfrac{5}{2}$ is in the form of $\dfrac{p}{q}$ as well as 5 and 2 are integers.

So, assertion (A) is true.

According to commutative property of addition: When two numbers are added together, then a change in their positions does not change the result.

When $\dfrac{p}{q} \text{ and } \dfrac{r}{s}$ are any two rational numbers then $\dfrac{p}{q} + \dfrac{r}{s} = \dfrac{r}{s} + \dfrac{p}{q}$, as addition of rational numbers is a commutative property.

So, reason (R) is true but it does not explain assertion.

Hence, option 2 is the correct option.