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}`
(b) Find the domain of R.

Answer

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

### Step 1: Identify the elements of set A
Set \( A \) is given as:
\[ A = \{1, 2, 3, 4\} \]

### Step 2: Understand the relation R
The relation \( R \) consists of ordered pairs \( (x, y) \) where \( x \) is an element from set \( A \) and \( y \) is defined as \( y = x^2 \). This means for each \( x \) in \( A \), we will calculate \( y \).

### Step 3: Calculate the ordered pairs
Now, we compute \( y \) for each \( x \) in \( A \):
- For \( x = 1 \): \( y = 1^2 = 1 \) → Ordered pair: \( (1, 1) \)
- For \( x = 2 \): \( y = 2^2 = 4 \) → Ordered pair: \( (2, 4) \)
- For \( x = 3 \): \( y = 3^2 = 9 \) → Ordered pair: \( (3, 9) \)
- For \( x = 4 \): \( y = 4^2 = 16 \) → Ordered pair: \( (4, 16) \)

Thus, the relation \( R \) can be expressed as:
\[ R = \{(1, 1), (2, 4), (3, 9), (4, 16)\} \]

### Step 4: Determine the domain of R
The domain of a relation is the set of all first elements (or \( x \)-values) from the ordered pairs in the relation. From our calculated pairs, the first elements are:
- From \( (1, 1) \): \( 1 \)
- From \( (2, 4) \): \( 2 \)
- From \( (3, 9) \): \( 3 \)
- From \( (4, 16) \): \( 4 \)

Thus, the domain of \( R \) is:
\[ \text{Domain of } R = \{1, 2, 3, 4\} \]

### Final Answer
The domain of the relation \( R \) is:
\[ \{1, 2, 3, 4\} \]

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