Which one of the following is not true?

Options

A. `A - B sube A`
B. `B' - A' sube A`
C. `A sube A - B`
D. `A nn B' sube A`

Explanation

To determine which statement is not true among the given options, we will analyze each statement step by step.

### Step 1: Understand the Sets
Let’s define two sets:
- Let \( A \) be a set of elements.
- Let \( B \) be another set of elements.

### Step 2: Analyze Each Statement

1. **Statement 1: \( A - B \subseteq A \)**
- The expression \( A - B \) represents the set of elements that are in \( A \) but not in \( B \).
- Since all elements of \( A - B \) are derived from \( A \), it follows that \( A - B \) is indeed a subset of \( A \).
- **Conclusion**: This statement is true.

2. **Statement 2: \( B' - A' \subseteq A \)**
- Here, \( B' \) (or \( B^c \)) represents the complement of set \( B \), which includes all elements not in \( B \).
- The expression \( B' - A' \) represents the elements that are in \( B' \) but not in \( A' \).
- Since \( A' \) includes elements not in \( A \), removing \( A' \) from \( B' \) will still leave us with elements that are not in \( B \) and could potentially be in \( A \).
- Therefore, \( B' - A' \) can still include elements that are not in \( A \).
- **Conclusion**: This statement is not necessarily true.

3. **Statement 3: \( A \subseteq A - B \)**
- This statement claims that \( A \) is a subset of \( A - B \).
- However, \( A - B \) consists of elements in \( A \) that are not in \( B \). Therefore, if an element is in \( B \), it cannot be in \( A - B \).
- This means that \( A \) cannot be a subset of \( A - B \) since there could be elements in \( A \) that are also in \( B \).
- **Conclusion**: This statement is false.

4. **Statement 4: \( A \cap B' \subseteq A \)**
- The expression \( A \cap B' \) represents the intersection of set \( A \) with the complement of \( B \).
- This means we are looking at elements that are in \( A \) and not in \( B \).
- Since all elements in \( A \cap B' \) are also in \( A \), this statement is true.
- **Conclusion**: This statement is true.

### Final Conclusion
From the analysis:
- Statement 1 is true.
- Statement 2 is not necessarily true.
- Statement 3 is false.
- Statement 4 is true.

Thus, the statement that is **not true** is **Statement 3: \( A \subseteq A - B \)**.