Let A = {-1, 2, 5, 8}, B = {0, 1, 3, 6, 7} and R be the relation is one less than from A to B then how many elements will R contain?

Options

A. A. 2
B. B. 3
C. C. 5
D. D. 9

Answer

To solve the problem, we need to determine how many elements the relation \( R \) contains, where \( R \) is defined as the relation where each element in set \( A \) is one less than an element in set \( B \).

### Step-by-Step Solution:

1. **Identify the Sets**:
- Set \( A = \{-1, 2, 5, 8\} \)
- Set \( B = \{0, 1, 3, 6, 7\} \)

2. **Define the Relation**:
- The relation \( R \) consists of pairs \( (a, b) \) such that \( b = a + 1 \) for \( a \in A \) and \( b \in B \).

3. **Check Each Element in Set \( B \)**:
- For each element \( b \) in set \( B \), we need to find if there exists an \( a \) in set \( A \) such that \( a = b - 1 \).

4. **Evaluate Each Element in \( B \)**:
- **For \( b = 0 \)**:
- \( a = 0 - 1 = -1 \) (which is in \( A \))
- So, the pair \( (-1, 0) \) is in \( R \).
- **For \( b = 1 \)**:
- \( a = 1 - 1 = 0 \) (which is not in \( A \))
- So, no pair for \( b = 1 \).
- **For \( b = 3 \)**:
- \( a = 3 - 1 = 2 \) (which is in \( A \))
- So, the pair \( (2, 3) \) is in \( R \).
- **For \( b = 6 \)**:
- \( a = 6 - 1 = 5 \) (which is in \( A \))
- So, the pair \( (5, 6) \) is in \( R \).
- **For \( b = 7 \)**:
- \( a = 7 - 1 = 6 \) (which is not in \( A \))
- So, no pair for \( b = 7 \).

5. **List the Pairs in Relation \( R \)**:
- From the evaluations, we found the following pairs:
- \( (-1, 0) \)
- \( (2, 3) \)
- \( (5, 6) \)

6. **Count the Elements in \( R \)**:
- The pairs in \( R \) are \( (-1, 0) \), \( (2, 3) \), and \( (5, 6) \).
- Therefore, \( R \) contains **3 elements**.

### Final Answer:
The relation \( R \) contains **3 elements**.