Give an example of a relation. Which is
(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

Explanation

To solve the question, we need to provide examples of relations that satisfy specific properties: symmetric, transitive, and reflexive. Let's go through each part step by step.

### (i) Symmetric but neither reflexive nor transitive.

**Example:**
Let \( A = \{1, 2, 3\} \) and define the relation \( S_1 = \{(1, 2), (2, 1)\} \).

**Explanation:**
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