For the following relation
`R = {(0,0),(0,1),(1,1),(2,1),(2,2),(2,0),(1,0), (0,2),(0,1) }`

Options

A. domain = {0,1}
B. range = {0,1,2}
C. both correct
D. None of these

Answer

To find the domain and range of the relation \( R = \{(0,0),(0,1),(1,1),(2,1),(2,2),(2,0),(1,0), (0,2),(0,1)\} \), we will follow these steps:

### Step 1: Identify the Domain
The domain of a relation consists of all the first elements (x-coordinates) of the ordered pairs.

- From the relation \( R \), we have the following x-coordinates:
- From (0,0) → 0
- From (0,1) → 0
- From (1,1) → 1
- From (2,1) → 2
- From (2,2) → 2
- From (2,0) → 2
- From (1,0) → 1
- From (0,2) → 0
- From (0,1) → 0

Now, we will collect the unique x-coordinates:
- Unique x-coordinates are: 0, 1, 2

Thus, the domain is:
\[ \text{Domain} = \{0, 1, 2\} \]

### Step 2: Identify the Range
The range of a relation consists of all the second elements (y-coordinates) of the ordered pairs.

- From the relation \( R \), we have the following y-coordinates:
- From (0,0) → 0
- From (0,1) → 1
- From (1,1) → 1
- From (2,1) → 1
- From (2,2) → 2
- From (2,0) → 0
- From (1,0) → 0
- From (0,2) → 2
- From (0,1) → 1

Now, we will collect the unique y-coordinates:
- Unique y-coordinates are: 0, 1, 2

Thus, the range is:
\[ \text{Range} = \{0, 1, 2\} \]

### Final Answer
- Domain: \(\{0, 1, 2\}\)
- Range: \(\{0, 1, 2\}\)

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