If `R = {{2,a),(3,c),(9,b),(7,a), (8,a), (1,d)}`, then `R^(-1)` is equal to

Options

A. {(a,2),(a,7),(a,8),(b,9),(c,3),(d,1)}
B. {(a,2),(b,9),(c,2),(d,1)}
C. {(a,7),(a,8),(c,2),(d,1)}
D. {(a,2),(b,9),(c,3),(d,1)}

Answer

To find the inverse of the relation \( R \), we need to reverse the ordered pairs in the relation. The relation \( R \) is given as:

\[ R = \{(2, a), (3, c), (9, b), (7, a), (8, a), (1, d)\} \]

### Step-by-Step Solution:

1. **Identify the Ordered Pairs**:
The relation \( R \) consists of the following ordered pairs:
- \( (2, a) \)
- \( (3, c) \)
- \( (9, b) \)
- \( (7, a) \)
- \( (8, a) \)
- \( (1, d) \)

2. **Reverse Each Ordered Pair**:
To find the inverse relation \( R^{-1} \), we will reverse each of the ordered pairs:
- The pair \( (2, a) \) becomes \( (a, 2) \)
- The pair \( (3, c) \) becomes \( (c, 3) \)
- The pair \( (9, b) \) becomes \( (b, 9) \)
- The pair \( (7, a) \) becomes \( (a, 7) \)
- The pair \( (8, a) \) becomes \( (a, 8) \)
- The pair \( (1, d) \) becomes \( (d, 1) \)

3. **Combine the Reversed Pairs**:
Now, we will combine all the reversed pairs into the inverse relation:
\[ R^{-1} = \{(a, 2), (c, 3), (b, 9), (a, 7), (a, 8), (d, 1)\} \]

4. **Final Result**:
Thus, the inverse of the relation \( R \) is:
\[ R^{-1} = \{(a, 2), (c, 3), (b, 9), (a, 7), (a, 8), (d, 1)\} \]