Let A={1,2,3,4},B={1,4,9,16,25} and R be a relation defined from A to B as , `R ={(x,y):x in A and y =x^2}`
(d) write codomain of R.

Answer

To find the codomain of the relation \( R \) defined from set \( A \) to set \( B \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sets**:
- Set \( A = \{1, 2, 3, 4\} \)
- Set \( B = \{1, 4, 9, 16, 25\} \)

2. **Define the Relation \( R \)**:
- The relation \( R \) is defined as \( R = \{(x, y) : x \in A \text{ and } y = x^2\} \).
- This means for each element \( x \) in set \( A \), we will find \( y \) by squaring \( x \).

3. **Calculate the Values of \( y \)**:
- For \( x = 1 \): \( y = 1^2 = 1 \)
- For \( x = 2 \): \( y = 2^2 = 4 \)
- For \( x = 3 \): \( y = 3^2 = 9 \)
- For \( x = 4 \): \( y = 4^2 = 16 \)

4. **List the Ordered Pairs in Relation \( R \)**:
- The relation \( R \) can be expressed as:
\[ R = \{(1, 1), (2, 4), (3, 9), (4, 16)\} \]

5. **Determine the Codomain**:
- The codomain of a relation is the set from which the second elements of the ordered pairs are drawn.
- In this case, since \( R \) is defined from \( A \) to \( B \), the codomain of \( R \) is the entire set \( B \).

6. **Conclusion**:
- Therefore, the codomain of the relation \( R \) is:
\[ \text{Codomain of } R = B = \{1, 4, 9, 16, 25\} \]