If A={a,b,c,d}, then on A .
(i) write the identity relation `I_(A)` .
(ii) write a reflexive relation which is not the identity relation.

Answer

To solve the given problem, we will address each part step by step.

### Step 1: Write the identity relation \( I_A \)

The identity relation on a set is defined as the set of all ordered pairs where each element is related to itself.

Given the set \( A = \{a, b, c, d\} \), the identity relation \( I_A \) will include the following pairs:

- \( (a, a) \)
- \( (b, b) \)
- \( (c, c) \)
- \( (d, d) \)

Thus, the identity relation \( I_A \) can be written as:
\[ I_A = \{(a, a), (b, b), (c, c), (d, d)\} \]

### Step 2: Write a reflexive relation which is not the identity relation

A reflexive relation on a set is one where every element is related to itself, but it can also include additional pairs that do not conform to the identity relation.

We can create a reflexive relation by including all the pairs from the identity relation and adding some extra pairs. For example, we can add the pairs \( (a, c) \) and \( (b, d) \) to the identity relation.

Thus, a reflexive relation that is not the identity relation can be written as:
\[ R = \{(a, a), (b, b), (c, c), (d, d), (a, c), (b, d)\} \]

### Final Answers

1. The identity relation \( I_A \) is:
\[ I_A = \{(a, a), (b, b), (c, c), (d, d)\} \]

2. A reflexive relation which is not the identity relation is:
\[ R = \{(a, a), (b, b), (c, c), (d, d), (a, c), (b, d)\} \]