If A, B and C are three sets, then
`(A -B) cap (B-C) cap (C-A)` is equal to:

Options

A. `A cap B cap C`
B. `A' cap B' cap C'`
C. `phi`
D. `A cap B' capC`

Answer

To solve the problem `(A - B) ∩ (B - C) ∩ (C - A)`, we will break it down step by step.

### Step 1: Understand the Set Operations
- **Set Difference**: The operation `A - B` means the elements that are in set A but not in set B.
- **Intersection**: The operation `∩` means we are looking for common elements between the sets.

### Step 2: Calculate Each Set Difference
1. **Calculate A - B**: This set includes all elements that are in A but not in B.
2. **Calculate B - C**: This set includes all elements that are in B but not in C.
3. **Calculate C - A**: This set includes all elements that are in C but not in A.

### Step 3: Visualize the Sets
- Draw a Venn diagram with three overlapping circles representing sets A, B, and C.
- Identify the regions for each of the differences:
- The region for `A - B` will be the part of A that does not overlap with B.
- The region for `B - C` will be the part of B that does not overlap with C.
- The region for `C - A` will be the part of C that does not overlap with A.

### Step 4: Find the Intersection
- Now, we need to find the intersection of the three sets: `(A - B) ∩ (B - C) ∩ (C - A)`.
- Look for common elements in the regions identified in the Venn diagram.
- Since each of these regions represents elements that are unique to each set, there will be no common elements among them.

### Step 5: Conclusion
- Since there are no common elements in the intersection of these three sets, we conclude that:
\[ (A - B) ∩ (B - C) ∩ (C - A) = \emptyset \]
- Therefore, the answer is the empty set.

### Final Answer
\[ (A - B) ∩ (B - C) ∩ (C - A) = \emptyset \]