The relation R from A to B is given as `R = {(1, 2), (2, 5), ((1)/(2), 7)}`. The domain of R is

Options

A. {1, 2}
B. {2, 5, 7}
C. `{1, 2, (1)/(2)}`
D. `{1, 2, 5, (1)/(2), 7}`

Answer

To find the domain of the relation \( R = \{(1, 2), (2, 5), \left(\frac{1}{2}, 7\right)\} \), we will follow these steps:

### Step 1: Understand the Relation
The relation \( R \) consists of ordered pairs where the first element of each pair represents an input from set \( A \) and the second element represents an output in set \( B \).

### Step 2: Identify the First Elements
To find the domain, we need to extract the first elements from each ordered pair in the relation \( R \).

### Step 3: List the First Elements
The ordered pairs in \( R \) are:
- \( (1, 2) \)
- \( (2, 5) \)
- \( \left(\frac{1}{2}, 7\right) \)

From these pairs, the first elements are:
- From \( (1, 2) \), the first element is \( 1 \).
- From \( (2, 5) \), the first element is \( 2 \).
- From \( \left(\frac{1}{2}, 7\right) \), the first element is \( \frac{1}{2} \).

### Step 4: Compile the Domain
Now, we compile the unique first elements to form the domain of the relation \( R \):
- The domain is \( \{1, 2, \frac{1}{2}\} \).

### Final Answer
Thus, the domain of the relation \( R \) is \( \{1, 2, \frac{1}{2}\} \).

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