Let A and B be two non-empty subsets of a set X such that A is not a subset of B then

Options

A. A is a subset of complement of B
B. B is a subset of A
C. A and B are Disjoint
D. A and the complement of bare non- disjoint .

Answer

To solve the problem, we need to analyze the given statement: "Let A and B be two non-empty subsets of a set X such that A is not a subset of B." We need to determine the implications of this statement and evaluate the possible options.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We have two non-empty subsets A and B of a set X.
- It is stated that A is not a subset of B. This means there exists at least one element in A that is not in B.

2. **Finding Elements in A and B**:
- Let's assume some elements for A and B to illustrate the concept.
- For example, let \( A = \{2, 5, 7\} \) and \( B = \{1, 5, 6\} \).
- Here, we can see that A contains the elements 2 and 7 which are not in B.

3. **Checking Subset Relationships**:
- Since A is not a subset of B, we confirm that there are elements in A that do not belong to B.
- We also check if B is a subset of A. In our example, B contains the element 1 which is not in A, so B is also not a subset of A.

4. **Exploring the Complement of B**:
- The complement of B, denoted as \( B' \), consists of all elements in X that are not in B.
- If \( X = \{1, 2, 3, 4, 5, 6, 7\} \), then \( B' = \{2, 3, 4, 7\} \).

5. **Analyzing the Relationship Between A and B'**:
- We need to check if A is a subset of \( B' \) or if A and \( B' \) are disjoint.
- In our example, A has elements 2 and 7 which are also in \( B' \). Therefore, A is not a subset of \( B' \) since it contains the element 5 which is not in \( B' \).

6. **Conclusion**:
- Since A is not a subset of B and we have found elements that are common between A and \( B' \), we conclude that A and \( B' \) are non-disjoint.
- Thus, we can summarize that A and B have some common elements, and A is not a subset of B.

### Final Answer:
The correct conclusion is that A and \( B' \) are non-disjoint.