Let `A` be the set of all human beings in a town at a particular time. Determine whether Relation `R={(x ,\ y): x` and `y` work at the same place} is reflexive, symmetric and transitive:

Explanation

To determine whether the relation \( R = \{(x, y) : x \text{ and } y \text{ work at the same place}\} \) is reflexive, symmetric, and transitive, we will analyze each property step by step.

### Step 1: Check for Reflexivity
A relation \( R \) is reflexive if for every element \( x \in A \), the pair \( (x, x) \) is in \( R \).

- For any person \( x \) in the set \( A \) (the set of all human beings in the town), it is true that \( x \) works at the same place as themselves.
- Therefore, \( (x, x) \) belongs to \( R \).

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