If A = {2, 4, 6}, then domain of the relation R defined on A is

Options

A. {2, 4}
B. {4, 6}
C. {(2,6)
D. {2, 4, 6}

Answer

To find the domain of the relation \( R \) defined on the set \( A = \{2, 4, 6\} \), we can follow these steps:

### Step 1: Understand the Definition of a Relation
A relation \( R \) from set \( A \) to set \( A \) is a subset of the Cartesian product \( A \times A \). This means that \( R \) consists of ordered pairs where both elements come from the set \( A \).

### Step 2: Determine the Cartesian Product \( A \times A \)
The Cartesian product \( A \times A \) is calculated by pairing each element of \( A \) with every element of \( A \):
\[ A \times A = \{(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)\} \]

### Step 3: Identify the Domain of the Relation
The domain of a relation is the set of all first elements from the ordered pairs in the relation. Since we are considering all possible pairs from \( A \times A \), the domain will include all elements of \( A \):
- From the pairs, the first elements are \( 2, 4, \) and \( 6 \).

### Step 4: Write the Domain
Thus, the domain of the relation \( R \) defined on \( A \) is:
\[ \text{Domain}(R) = \{2, 4, 6\} \]

### Conclusion
The domain of the relation \( R \) defined on the set \( A \) is \( \{2, 4, 6\} \).

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