Let `A=[3,4] and B[7,11]` and R be the relation from A to B defined as `R={(a,b): a in A, b in B, a-b` is odd then

Options

A. `R=RxxB`
B. `R=phi`
C. `RsubAxxB`
D. `Rsub BxxA`

Answer

To solve the problem, we need to determine the relation \( R \) from set \( A \) to set \( B \) defined as \( R = \{(a, b) : a \in A, b \in B, a - b \text{ is odd}\} \).

### Step-by-Step Solution:

1. **Identify the Elements of Sets A and B**:
- Set \( A = \{3, 4\} \)
- Set \( B = \{7, 11\} \)

2. **Determine the Possible Pairs (a, b)**:
- We will consider all combinations of elements from set \( A \) and set \( B \):
- Pair (3, 7)
- Pair (3, 11)
- Pair (4, 7)
- Pair (4, 11)

3. **Check Each Pair to See if \( a - b \) is Odd**:
- For the pair (3, 7):
\[ 3 - 7 = -4 \quad (\text{even}) \]
- For the pair (3, 11):
\[ 3 - 11 = -8 \quad (\text{even}) \]
- For the pair (4, 7):
\[ 4 - 7 = -3 \quad (\text{odd}) \]
- For the pair (4, 11):
\[ 4 - 11 = -7 \quad (\text{odd}) \]

4. **Collect the Valid Pairs**:
- From the checks above, the pairs where \( a - b \) is odd are:
- (4, 7)
- (4, 11)

5. **Define the Relation R**:
- Thus, the relation \( R \) can be defined as:
\[ R = \{(4, 7), (4, 11)\} \]

### Final Answer:
The relation \( R \) is \( \{(4, 7), (4, 11)\} \).

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