If A and B are finite sets, which of the following is the correct statement.

Options

A. `n (A - B) = n (A) `
B. ` n(A-B) = n (B - A) `
C. ` n (A-B) = n ( A) -n (A nn B) `
D. ` n ( A - B) = n (B) - n (A nn B ) `

Explanation

To solve the question regarding finite sets A and B, we need to analyze the given options using the concept of set operations and Venn diagrams. Let's break down the solution step by step.

### Step-by-Step Solution

1. **Understanding Finite Sets**:
- Finite sets are those that contain a limited or countable number of elements. For example, if A = {1, 2, 3} and B = {2, 3, 4}, both A and B are finite sets.

**Hint**: Remember that a finite set has a specific number of elements, unlike infinite sets.

2. **Identifying Set Operations**:
- We need to analyze the operations A - B, B - A, A ∩ B (intersection), and their relationships.

3. **Using Venn Diagrams**:
- Draw a Venn diagram with two overlapping circles, one for set A and one for set B. The overlapping area represents A ∩ B (the intersection).

**Hint**: Visualizing with a Venn diagram can help clarify how the sets relate to each other.

4. **Analyzing Option 1 (A - B)**:
- A - B represents the elements that are in A but not in B. In the Venn diagram, this is the part of circle A that does not overlap with circle B.
- This option states that the number of elements in A - B is equal to the number of elements in A, which is incorrect because A - B excludes elements that are also in B.

**Hint**: A - B cannot equal A unless B is an empty set.

5. **Analyzing Option 2 (B - A)**:
- B - A represents the elements that are in B but not in A. This is the part of circle B that does not overlap with circle A.
- Similar to Option 1, this option states that the number of elements in B - A is equal to the number of elements in B, which is also incorrect for the same reason.

**Hint**: B - A cannot equal B unless A is an empty set.

6. **Analyzing Option 3 (A ∩ B)**:
- A ∩ B represents the elements that are common to both A and B. The number of elements in A - A ∩ B would be the elements in A that are not in the intersection.
- This option correctly states that the number of elements in A - B is equal to the number of elements in A minus the number of elements in the intersection, which is a valid statement.

**Hint**: The intersection affects the count of elements in both sets.

7. **Analyzing Option 4 (B - A)**:
- This option states that the number of elements in B - A is equal to the number of elements in B minus the number of elements in the intersection. This is incorrect as it does not match the required condition.

**Hint**: Always check if the operation matches the definition.

8. **Conclusion**:
- After analyzing all options, we find that **Option 3** is the correct statement: the number of elements in A - B is equal to the number of elements in A minus the number of elements in the intersection of A and B.

### Final Answer
The correct statement is: **The number of elements in A - B is equal to the number of elements in A minus the number of elements in A ∩ B.**