Let R be a relation defined on set `A={1, 2, 3,4,5,6,7,8}` such that `R={(2,3)(4,5)(7,8)}`. If the domain of R is set B and range is set C then `BnnC` is

Options

A. `phi`
B. {2, 4, 7}
C. {3, 5, 8}
D. {3}

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the sets
We are given the set \( A = \{1, 2, 3, 4, 5, 6, 7, 8\} \) and the relation \( R = \{(2, 3), (4, 5), (7, 8)\} \).

### Step 2: Determine the domain and range of the relation \( R \)
The domain of a relation consists of the first elements of each ordered pair in \( R \), while the range consists of the second elements.

- **Domain (Set B)**: From \( R \), the first elements are \( 2, 4, 7 \). Therefore,
\[ B = \{2, 4, 7\} \]

- **Range (Set C)**: From \( R \), the second elements are \( 3, 5, 8 \). Therefore,
\[ C = \{3, 5, 8\} \]

### Step 3: Find the intersection of sets \( B \) and \( C \)
The intersection of two sets consists of the elements that are common to both sets.

- **Intersection \( B \cap C \)**: We need to find elements that are present in both \( B \) and \( C \).
- Elements in \( B \): \( 2, 4, 7 \)
- Elements in \( C \): \( 3, 5, 8 \)

Since there are no common elements between sets \( B \) and \( C \), we have:
\[ B \cap C = \emptyset \]

### Step 4: Conclusion
Since the intersection is empty, we can conclude that:
\[ B \cap C = \emptyset \]

### Final Answer
Thus, the answer to the question is that \( B \cap C \) is the empty set.

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