If A={a,y} and B={2,5} , then find the number of relations from set A to B.

Answer

To find the number of relations from set A to set B, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sets**:
- We have set A = {a, y} and set B = {2, 5}.

2. **Count the Elements in Each Set**:
- The number of elements in set A (denoted as m) is 2 (since A has 'a' and 'y').
- The number of elements in set B (denoted as n) is also 2 (since B has '2' and '5').

3. **Use the Formula for Relations**:
- The number of relations from set A to set B can be calculated using the formula \( 2^{mn} \), where m is the number of elements in set A and n is the number of elements in set B.

4. **Calculate mn**:
- Here, \( m = 2 \) and \( n = 2 \), so \( mn = 2 \times 2 = 4 \).

5. **Calculate the Number of Relations**:
- Now, substitute \( mn \) into the formula:
\[ 2^{mn} = 2^4 \]
- Calculate \( 2^4 \):
\[ 2^4 = 16 \]

6. **Conclusion**:
- Therefore, the number of relations from set A to set B is 16.

### Final Answer:
The number of relations from set A to set B is **16**.