Let `A={1,2,3}` and `R={(1,2),(1,1),(2,3)}` be a relation on `A` . What minimum number of ordered pairs may be added to `R` so that it may become a transitive relation on `Adot`

Explanation

To determine the minimum number of ordered pairs that need to be added to the relation \( R \) so that it becomes a transitive relation on the set \( A = \{1, 2, 3\} \), we will follow these steps:

### Step 1: Understand the given relation
The relation \( R \) is given as:
\[ R = \{(1, 2), (1, 1), (2, 3)\} \]
We need to check if this relation is transitive and if not, find out what pairs need to be added.
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