Let R be the relation in the set of integers Z given by R = {(a, b): 2 divides a - b}.
Assertion (A): R is a reflexive relation. Reason
(R): A relation is said to be reflexive `x Rx, AA x in Z`.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is True

Answer

To determine whether the relation \( R \) defined by \( R = \{(a, b) : 2 \text{ divides } (a - b)\} \) is reflexive, we need to check if it satisfies the condition for reflexivity.

### Step-by-Step Solution:

1. **Understanding Reflexivity**: A relation \( R \) on a set is said to be reflexive if for every element \( x \) in the set, the pair \( (x, x) \) is in the relation \( R \). In mathematical terms, \( \forall x \in Z, (x, x) \in R \).

2. **Applying the Definition to Our Relation**: For our specific relation \( R \), we need to check if \( (a, a) \) is in \( R \) for every integer \( a \). This means we need to check if \( 2 \) divides \( a - a \).

3. **Calculating \( a - a \)**: We know that \( a - a = 0 \).

4. **Checking Divisibility**: Now, we check if \( 2 \) divides \( 0 \). Since \( 0 \) can be expressed as \( 2 \times 0 \), it is clear that \( 2 \) divides \( 0 \).

5. **Conclusion**: Since \( (a, a) \) is in \( R \) for every integer \( a \), we conclude that the relation \( R \) is reflexive.

### Final Answer:
The assertion (A) that \( R \) is a reflexive relation is true.