State for each of the following relations whether it is function or not. (Write Yes or No)
`{(x,y):x inA,yinB" is surname of x"}` where A is the set of people in India and B is the set of surnames.

Answer

To determine whether the relation \(\{(x,y): x \in A, y \in B \text{ is surname of } x\}\) is a function, we need to analyze the definition of a function in the context of this relation.

### Step-by-Step Solution:

1. **Understanding the Sets**:
- Let \(A\) be the set of all people in India.
- Let \(B\) be the set of all surnames.

2. **Definition of a Function**:
- A relation is a function if every element in the domain (set \(A\) in this case) is associated with exactly one element in the codomain (set \(B\)).
- This means that for each person \(x\) in set \(A\), there should be only one unique surname \(y\) in set \(B\).

3. **Analyzing the Relation**:
- In India, multiple people can share the same surname. For example, many individuals may have the surname "Sharma" or "Patel".
- This implies that a single surname can correspond to multiple individuals.

4. **Conclusion**:
- Since a single person may not have a unique surname (as many people can share the same surname), the relation does not satisfy the definition of a function.
- Therefore, the relation is **not a function**.

### Final Answer:
**No**, the relation is not a function.