A, B and C are three non-empty sets. If `A sub B and B subC` then which the following is true?

Options

A. `B-A=C-B`
B. `AnnBnnC=B`
C. `AuuB=BnnC`
D. `AuuBuuC=A`

Answer

To solve the problem, we need to analyze the relationships between the sets A, B, and C given that A is a subset of B and B is a subset of C.

### Step-by-Step Solution:

1. **Understand the Relationships**:
- We are given that \( A \subseteq B \) and \( B \subseteq C \).
- This means every element of A is also an element of B, and every element of B is also an element of C.

2. **Visual Representation**:
- We can visualize this using a Venn diagram:
- Draw three circles: one for A, one for B, and one for C.
- Circle A is completely inside circle B, and circle B is completely inside circle C.

3. **Intersection of Sets**:
- The intersection of sets \( A \cap B \cap C \):
- Since A is a subset of B, and B is a subset of C, the intersection \( A \cap B \cap C \) will be equal to A.
- Therefore, \( A \cap B \cap C = A \).

4. **Union of Sets**:
- The union of sets \( A \cup B \cup C \):
- Since A is contained in B and B is contained in C, the union of all three sets will be equal to C.
- Therefore, \( A \cup B \cup C = C \).

5. **Other Relationships**:
- The union of A and B, \( A \cup B \):
- Since A is a subset of B, \( A \cup B = B \).
- The intersection of B and C, \( B \cap C \):
- Since B is a subset of C, \( B \cap C = B \).

6. **Conclusion**:
- From the above analysis, we can conclude:
- \( A \cap B \cap C = A \)
- \( A \cup B \cup C = C \)
- \( A \cup B = B \)
- \( B \cap C = B \)

### Final Answer:
Given the relationships, the true statements are:
- \( A \cap B \cap C = A \)
- \( A \cup B \cup C = C \)