Let A and B be two non empty subsets of 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 sets
D. A and complement of B are non-disjoint sets

Explanation

To solve the problem, we need to analyze the given information and the options provided. We have two non-empty subsets \( A \) and \( B \) of a set \( X \) such that \( A \) is not a subset of \( B \). This means that there exists at least one element in \( A \) that is not in \( B \).

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We know that \( A \) is not a subset of \( B \). This implies that there exists at least one element \( x \in A \) such that \( x \notin B \).

2. **Analyzing the Options**:
- We need to evaluate the four options provided:
1. \( A \subseteq \overline{B} \) (A is a subset of the complement of B)
2. \( B \subseteq A \) (B is a subset of A)
3. \( A \) and \( B \) are disjoint sets
4. \( A \) and \( \overline{B} \) are non-disjoint sets

3. **Evaluating Each Option**:
- **Option 1**: \( A \subseteq \overline{B} \)
- This option suggests that all elements of \( A \) are outside of \( B \). However, we cannot conclude this from the information given. There may be elements in \( A \) that are also in \( B \). Thus, this option is not necessarily true.

- **Option 2**: \( B \subseteq A \)
- This option suggests that all elements of \( B \) are in \( A \). Again, we cannot conclude this from the information given. Therefore, this option is also not necessarily true.

- **Option 3**: \( A \) and \( B \) are disjoint sets
- For \( A \) and \( B \) to be disjoint, their intersection must be empty. Since we know that \( A \) contains at least one element that is not in \( B \), we cannot conclude that \( A \) and \( B \) are disjoint. Thus, this option is not necessarily true.

- **Option 4**: \( A \) and \( \overline{B} \) are non-disjoint sets
- The complement of \( B \), denoted \( \overline{B} \), consists of all elements in \( X \) that are not in \( B \). Since we have at least one element \( x \in A \) such that \( x \notin B \), it follows that \( x \) must be in \( \overline{B} \). Therefore, \( A \) and \( \overline{B} \) must have at least one element in common, making them non-disjoint.

4. **Conclusion**:
- The correct answer is that \( A \) and \( \overline{B} \) are non-disjoint sets.

### Final Answer:
The correct option is **4. \( A \) and \( \overline{B} \) are non-disjoint sets**.