Given `R={(x,y): x,y inZ,y=3}`, then which ordered pair belongs to R?

Options

A. (1,4)
B. (0,3)
C. (5,2)
D. (-4,1)

Answer

To solve the problem, we need to analyze the given relation \( R \) and determine which ordered pair belongs to it.

### Step-by-Step Solution:

1. **Understand the Relation**: The relation \( R \) is defined as:
\[ R = \{(x, y) : x, y \in \mathbb{Z}, y = 3\} \]
This means that for any ordered pair \( (x, y) \) to belong to \( R \), \( y \) must be equal to 3, and both \( x \) and \( y \) must be integers.

2. **Identify the Required Condition**: Since \( y \) must equal 3, we can express any ordered pair in \( R \) in the form:
\[ (x, 3) \]
where \( x \) can be any integer.

3. **Examine the Given Options**: The options provided are:
- (1, 4)
- (0, 3)
- (5, 2)
- (-4, 1)

4. **Check Each Option**:
- **Option (1, 4)**: Here, \( y = 4 \), which does not satisfy \( y = 3 \). So, this pair does not belong to \( R \).
- **Option (0, 3)**: Here, \( y = 3 \), which satisfies the condition. Since \( 0 \) is also an integer, this pair belongs to \( R \).
- **Option (5, 2)**: Here, \( y = 2 \), which does not satisfy \( y = 3 \). So, this pair does not belong to \( R \).
- **Option (-4, 1)**: Here, \( y = 1 \), which does not satisfy \( y = 3 \). So, this pair does not belong to \( R \).

5. **Conclusion**: The only ordered pair that belongs to the relation \( R \) is:
\[ (0, 3) \]

### Final Answer:
The ordered pair that belongs to \( R \) is \( (0, 3) \).