R is a relation on N given by
`R={(x,y):4x+3y=20}.` Which of the following belongs to R?

Options

A. (-4, 12)
B. (5, 0)
C. (3, 4)
D. (2, 4)

Explanation

To determine which ordered pair belongs to the relation \( R = \{(x,y) : 4x + 3y = 20\} \), we will check each provided option to see if it satisfies the equation while ensuring that both \( x \) and \( y \) are natural numbers.

### Step-by-Step Solution:

1. **Identify the Relation**: The relation is defined by the equation \( 4x + 3y = 20 \).

2. **Check Each Option**:
- **Option 1**: \( (-4, 12) \)
- Here, \( x = -4 \) which is not a natural number. Therefore, this option does not belong to \( R \).

- **Option 2**: \( (5, 0) \)
- Substitute \( x = 5 \) into the equation:
\[ 4(5) + 3y = 20 \implies 20 + 3y = 20 \implies 3y = 0 \implies y = 0 \]
Since \( y = 0 \) is not a natural number, this option does not belong to \( R \).

- **Option 3**: \( (3, 4) \)
- Substitute \( x = 3 \) into the equation:
\[ 4(3) + 3y = 20 \implies 12 + 3y = 20 \implies 3y = 8 \implies y = \frac{8}{3} \]
Since \( y = \frac{8}{3} \) is not a natural number, this option does not belong to \( R \).

- **Option 4**: \( (2, 4) \)
- Substitute \( x = 2 \) into the equation:
\[ 4(2) + 3y = 20 \implies 8 + 3y = 20 \implies 3y = 12 \implies y = 4 \]
Here, both \( x = 2 \) and \( y = 4 \) are natural numbers. Therefore, this option belongs to \( R \).

3. **Conclusion**: The only ordered pair that belongs to the relation \( R \) is \( (2, 4) \).

### Final Answer:
The ordered pair that belongs to the relation \( R \) is \( (2, 4) \).