If A and B are non empty sets and A' and B' represents their compliments respectively, then

Options

A. ` A - B = A' -B' `
B. ` A -A'=B - B'`
C. ` A -B =B'-A'`
D. ` A - B'=A'-B`

Explanation

To solve the problem, we need to analyze the relationships between the sets A, B, and their complements A' and B'. We will go through the options provided and determine which one is correct.

### Step-by-step Solution:

1. **Understanding Complements**:
- The complement of a set A, denoted as A', consists of all elements in the universal set U that are not in A. Therefore, A' = U - A.
- Similarly, B' = U - B.

2. **Analyzing Option 1**:
- The first option states that A - B = A' - B'.
- Let's express A - B using complements:
- A - B = A ∩ B' (elements in A but not in B).
- A' - B' = (U - A) ∩ (U - B) = U - (A ∪ B).
- These two expressions are not equal, so Option 1 is incorrect.

3. **Analyzing Option 2**:
- The second option states that A - A' = B - B'.
- A - A' = A ∩ A' = ∅ (the intersection of a set and its complement is the empty set).
- Similarly, B - B' = B ∩ B' = ∅.
- Since both sides are equal to the empty set, Option 2 is correct.

4. **Analyzing Option 3**:
- The third option states that A - B = B' - A'.
- We already established that A - B = A ∩ B'.
- Now, let's express B' - A':
- B' - A' = (U - B) - (U - A) = A - B.
- Therefore, Option 3 is also correct.

5. **Analyzing Option 4**:
- The fourth option states that A - B' = B - A'.
- A - B' = A ∩ B.
- B - A' = B ∩ A.
- Both expressions are equal, so Option 4 is correct.

### Conclusion:
- The correct options are **Option 2**, **Option 3**, and **Option 4**.