Write down the domain and range of the relation (x,y): x=3y and x and y are natural numbers less than 10.

Answer

To find the domain and range of the relation defined by the equation \( x = 3y \) where \( x \) and \( y \) are natural numbers less than 10, we will follow these steps:

### Step 1: Identify the natural numbers less than 10
Natural numbers less than 10 are:
\[ 1, 2, 3, 4, 5, 6, 7, 8, 9 \]

### Step 2: Express \( y \) in terms of \( x \)
From the equation \( x = 3y \), we can express \( y \) as:
\[ y = \frac{x}{3} \]

### Step 3: Determine possible values of \( x \)
Since \( x \) must also be a natural number less than 10, we will find the values of \( x \) that can be expressed as \( 3y \) where \( y \) is a natural number.

### Step 4: Calculate possible values of \( y \)
To ensure \( y \) is a natural number, \( x \) must be a multiple of 3. The multiples of 3 that are less than 10 are:
\[ 3, 6, 9 \]

### Step 5: Calculate corresponding values of \( y \)
Now, we will find the corresponding values of \( y \) for each value of \( x \):
- For \( x = 3 \):
\[ y = \frac{3}{3} = 1 \]
- For \( x = 6 \):
\[ y = \frac{6}{3} = 2 \]
- For \( x = 9 \):
\[ y = \frac{9}{3} = 3 \]

### Step 6: Write down the domain and range
Now we can write down the domain and range:
- **Domain** (values of \( x \)):
\[ \{3, 6, 9\} \]
- **Range** (values of \( y \)):
\[ \{1, 2, 3\} \]

### Final Answer
- **Domain**: \( \{3, 6, 9\} \)
- **Range**: \( \{1, 2, 3\} \)

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