If `A={1,\ 2,\ 3,\ 4}` define relations on `A` which have properties of being reflexive, symmetric and transitive.

Explanation

To define relations on the set \( A = \{1, 2, 3, 4\} \) that are reflexive, symmetric, and transitive, we need to ensure that the relations we create satisfy all three properties. Let's go through the steps to construct such a relation.

### Step 1: Ensure Reflexivity
A relation \( R \) on a set \( A \) is reflexive if every element in \( A \) is related to itself. This means we need to include the pairs \( (1, 1), (2, 2), (3, 3), (4, 4) \) in our relation \( R \).

**Relation so far:**
\[ R = \{(1, 1), (2, 2), (3, 3), (4, 4)\} \]

...