If A is a subset of B, then which one of the following is correct ?

Options

A. `A^(c)subeB^(c)`
B. `B^(c)subeA^(c)`
C. `A^(c)=B^(c)`
D. `AsubeAnnB`

Explanation

To solve the question "If A is a subset of B, then which one of the following is correct?", we will analyze the relationship between sets A and B, as well as their complements.

### Step-by-Step Solution:

1. **Understanding Subsets**:
- By definition, if \( A \) is a subset of \( B \) (denoted as \( A \subseteq B \)), it means that every element of \( A \) is also an element of \( B \).

2. **Defining Complements**:
- The complement of a set \( B \), denoted as \( B' \) or \( B^c \), includes all the elements in the universal set \( U \) that are not in \( B \).
- Similarly, the complement of set \( A \), denoted as \( A' \) or \( A^c \), includes all the elements in \( U \) that are not in \( A \).

3. **Analyzing Complements**:
- Since \( A \subseteq B \), it follows that all elements not in \( B \) (i.e., elements in \( B' \)) will also not be in \( A \). Therefore, \( B' \) contains elements that are not in \( A \).
- This implies that \( A' \) (elements not in \( A \)) will include all elements in \( B' \) (elements not in \( B \)), which means \( B' \subseteq A' \).

4. **Conclusion**:
- From the above analysis, we conclude that if \( A \subseteq B \), then \( B' \subseteq A' \) is a correct statement.

### Final Answer:
The correct statement is: **\( B' \subseteq A' \)**.

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