If `A subset B , B subset C` then

Options

A. `A subset C "necessarily"`
B. `A cancelsubset C "necessarily"`
C. A may not be sub-set of C
D. A=B

Answer

To solve the problem given the conditions \( A \subset B \) and \( B \subset C \), we need to analyze the implications of these subset relationships.

### Step-by-Step Solution:

1. **Understanding Subsets**:
- A set \( A \) is a subset of a set \( B \) (denoted \( A \subset B \)) if every element of \( A \) is also an element of \( B \).
- Similarly, \( B \subset C \) means every element of \( B \) is also an element of \( C \).

2. **Given Relationships**:
- We are given that \( A \subset B \) and \( B \subset C \).

3. **Transitive Property of Subsets**:
- The subset relationship is transitive, which means if \( A \subset B \) and \( B \subset C \), then it follows that \( A \subset C \).
- This means every element of \( A \) is also an element of \( C \) because all elements of \( A \) are in \( B \), and all elements of \( B \) are in \( C \).

4. **Conclusion**:
- Therefore, we can conclude that \( A \subset C \) necessarily.

5. **Identifying the Correct Option**:
- Based on our conclusion, the correct answer to the question is that \( A \) is a subset of \( C \) necessarily.

### Final Answer:
- The correct option is: \( A \subset C \) necessarily.