State for each of the following relations whether it is function or not. (Write Yes or No)
`{(x,y):x inA,yinB,y" is sewn onto y"}`, where A is the set of buttons and B is the set of shirts.

Answer

To determine whether the given relation is a function, we need to analyze the definition of a function and the specific relation provided.

### Step-by-Step Solution:

1. **Understanding the Relation**: The relation is defined as \( R = \{(x, y) : x \in A, y \in B, y \text{ is sewn onto } y'\} \), where \( A \) is the set of buttons and \( B \) is the set of shirts.

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 button (element of \( A \)), there should be one and only one shirt (element of \( B \)) that it is sewn onto.

3. **Analyzing the Relation**:
- If a button \( x \) can be sewn onto multiple shirts, then it would violate the definition of a function because one input (button) would correspond to multiple outputs (shirts).
- Conversely, if each button can only be sewn onto one specific shirt, then it satisfies the criteria for being a function.

4. **Conclusion**:
- Since the relation specifies that a button can only be sewn onto one shirt (as indicated in the transcript), we conclude that this relation does indeed meet the criteria for a function.

Therefore, the answer is **Yes**, this relation is a function.