If A, B and C are three sets such that `A supB supC,` then `(AuuBuuC)-(AnnBnnC)=`

Options

A. `A-B`
B. `B-C`
C. `A-C`
D. none of these

Answer

To solve the problem, we need to find the value of the expression \( (A \cup B \cup C) - (A \cap B \cap C) \) given that \( C \subseteq B \) and \( B \subseteq A \).

### Step-by-Step Solution:

1. **Understanding the Relationships Between the Sets**:
- We know that \( C \subseteq B \) means all elements of set \( C \) are also in set \( B \).
- Similarly, \( B \subseteq A \) means all elements of set \( B \) (and thus all elements of set \( C \)) are also in set \( A \).

2. **Finding \( A \cup B \cup C \)**:
- Since \( B \) and \( C \) are subsets of \( A \), the union of all three sets \( A \cup B \cup C \) can be simplified to just \( A \).
- Therefore, we have:
\[ A \cup B \cup C = A \]

3. **Finding \( A \cap B \cap C \)**:
- The intersection \( A \cap B \cap C \) consists of all elements that are common to sets \( A \), \( B \), and \( C \).
- Since \( C \) is a subset of \( B \) and \( B \) is a subset of \( A \), the intersection \( A \cap B \cap C \) is simply \( C \).
- Thus, we have:
\[ A \cap B \cap C = C \]

4. **Substituting Back into the Expression**:
- Now we substitute the results back into the original expression:
\[ (A \cup B \cup C) - (A \cap B \cap C) = A - C \]

5. **Final Result**:
- Therefore, the final result of the expression \( (A \cup B \cup C) - (A \cap B \cap C) \) is:
\[ A - C \]

### Conclusion:
The value of \( (A \cup B \cup C) - (A \cap B \cap C) \) is \( A - C \).