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}`
`(c)` Find the range of R.

Answer

To find the range of the relation \( R \) defined from set \( A \) to set \( B \) where \( R = \{(x,y) : x \in A \text{ and } y = x^2\} \), we will follow these steps:

### Step 1: Identify the sets
We have:
- Set \( A = \{1, 2, 3, 4\} \)
- Set \( B = \{1, 4, 9, 16, 25\} \)

### Step 2: Apply the relation
The relation \( R \) is defined such that for each \( x \in A \), \( y \) is calculated as \( y = x^2 \). We will calculate \( y \) for each element in set \( A \).

### Step 3: Calculate \( y \) for each \( x \)
- For \( x = 1 \):
\[ y = 1^2 = 1 \]
- For \( x = 2 \):
\[ y = 2^2 = 4 \]
- For \( x = 3 \):
\[ y = 3^2 = 9 \]
- For \( x = 4 \):
\[ y = 4^2 = 16 \]

### Step 4: Compile the range
Now we compile the values of \( y \) obtained from the calculations:
- When \( x = 1 \), \( y = 1 \)
- When \( x = 2 \), \( y = 4 \)
- When \( x = 3 \), \( y = 9 \)
- When \( x = 4 \), \( y = 16 \)

Thus, the range of the relation \( R \) is:
\[ \text{Range}(R) = \{1, 4, 9, 16\} \]

### Final Answer
The range of \( R \) is \( \{1, 4, 9, 16\} \).

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