Determine whether each of the following relations are reflexive, symmetric and transitive:
Relation R in the set A of human beings in a town at a particular time given by
R = {(x, y) : x and y work at the same place}

Explanation

To determine whether the relation \( R \) defined as \( R = \{(x, y) : x \text{ and } y \text{ work at the same place}\} \) 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 the set \( A \), the pair \( (x, x) \) is in \( R \).

- Since every person \( x \) works at the same place as themselves, we have \( (x, x) \in R \) for all \( x \in A \).
- Therefore, the relation \( R \) is reflexive.

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