If 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 R as a set of ordered pairs is

Options

A. {(-1,0), (2,3), (5, 6)}
B. {(-1,0), (2, 1), (8,7)}
C. {(0, 1), (2, 3), (6, 7)}
D. {(1, 2), (2,3), (5,6), (6, 7), (7,8)}

Answer

To find the relation \( R \) defined as "is one less than" from set \( A \) to set \( B \), we will follow these steps:

### Step 1: Identify the sets
We have:
- Set \( A = \{-1, 2, 5, 8\} \)
- Set \( B = \{0, 1, 3, 6, 7\} \)

### Step 2: Define the relation
The relation \( R \) is defined such that for each element \( a \) in set \( A \), we find an element \( b \) in set \( B \) such that \( b = a - 1 \).

### Step 3: Calculate the elements of \( R \)
Now we will calculate \( b \) for each \( a \) in \( A \):

1. For \( a = -1 \):
\[ b = -1 - 1 = -2 \quad (\text{not in } B) \]

2. For \( a = 2 \):
\[ b = 2 - 1 = 1 \quad (\text{in } B) \]
So, we have the ordered pair \( (2, 1) \).

3. For \( a = 5 \):
\[ b = 5 - 1 = 4 \quad (\text{not in } B) \]

4. For \( a = 8 \):
\[ b = 8 - 1 = 7 \quad (\text{in } B) \]
So, we have the ordered pair \( (8, 7) \).

### Step 4: Compile the ordered pairs
From our calculations, the valid ordered pairs in relation \( R \) are:
- \( (2, 1) \)
- \( (8, 7) \)

Thus, the relation \( R \) as a set of ordered pairs is:
\[ R = \{(2, 1), (8, 7)\} \]

### Final Answer
The relation \( R \) is:
\[ R = \{(2, 1), (8, 7)\} \]

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