Two finite sets A and B are such that `AsubB`, then which of the following is not correct?

Options

A. `a. AuuB=B`
B. b. `AnnB=A`
C. c. `A-B=phi`
D. d. `B-A=phi`

Answer

To solve the problem, we need to analyze the properties of two finite sets A and B, given that A is a subset of B (denoted as \( A \subseteq B \)). We will evaluate each of the provided options to determine which statement is not correct.

### Step-by-Step Solution:

1. **Understanding the relationship \( A \subseteq B \)**:
- Since \( A \) is a subset of \( B \), every element in \( A \) is also in \( B \). This implies that \( B \) contains all elements of \( A \) and possibly more.

2. **Evaluating Option A: \( A \cup B = B \)**:
- The union of sets \( A \) and \( B \) is defined as the set containing all elements that are in \( A \), in \( B \), or in both.
- Since \( A \) is a subset of \( B \), the union \( A \cup B \) will simply be \( B \).
- **Conclusion**: This statement is correct.

3. **Evaluating Option B: \( A \cap B = A \)**:
- The intersection of sets \( A \) and \( B \) is defined as the set containing all elements that are in both \( A \) and \( B \).
- Since all elements of \( A \) are in \( B \), the intersection \( A \cap B \) will be exactly \( A \).
- **Conclusion**: This statement is correct.

4. **Evaluating Option C: \( A - B = \emptyset \)**:
- The difference \( A - B \) represents the elements that are in \( A \) but not in \( B \).
- Since \( A \) is a subset of \( B \), there are no elements in \( A \) that are outside of \( B \).
- Therefore, \( A - B \) will indeed be the empty set \( \emptyset \).
- **Conclusion**: This statement is correct.

5. **Evaluating Option D: \( B - A = \emptyset \)**:
- The difference \( B - A \) represents the elements that are in \( B \) but not in \( A \).
- Since \( B \) may contain elements that are not in \( A \) (as \( A \) is just a subset of \( B \)), there will be elements in \( B \) that are not in \( A \).
- Thus, \( B - A \) cannot be the empty set \( \emptyset \).
- **Conclusion**: This statement is not correct.

### Final Answer:
The option that is not correct is **Option D: \( B - A = \emptyset \)**.