`A-B` is equal to

Options

A. `(AuuB)-(AnnB)`
B. `AnnB^(C )`
C. `AnnB`
D. `B-A`

Answer

To find \( A - B \), we need to understand the concept of set difference in set theory. Here’s a step-by-step solution:

### Step 1: Understand the Sets
Let’s denote two sets:
- Set \( A \)
- Set \( B \)

### Step 2: Define the Set Difference
The set difference \( A - B \) is defined as the set of elements that are in \( A \) but not in \( B \). Mathematically, it can be expressed as:
\[ A - B = \{ x \in A \mid x \notin B \} \]

### Step 3: Visualize with a Venn Diagram
To visualize this, we can use a Venn diagram:
- Draw two overlapping circles, one for set \( A \) and one for set \( B \).
- The area where the circles overlap represents \( A \cap B \) (the intersection of \( A \) and \( B \)).
- The entire area covered by both circles represents \( A \cup B \) (the union of \( A \) and \( B \)).

### Step 4: Identify the Elements in \( A - B \)
From the Venn diagram:
- The elements in set \( A \) that are not in set \( B \) are represented by the part of circle \( A \) that does not overlap with circle \( B \).

### Step 5: Write the Final Expression
Thus, the set difference \( A - B \) can be expressed as:
\[ A - B = A \setminus (A \cap B) \]
This means we take all elements in \( A \) and remove those that are also in \( B \).

### Conclusion
The final answer for \( A - B \) is:
\[ A - B = A \setminus (A \cap B) \]