If `A={w,o,l, f}, B={f,l,o,w}, C={f,o,w,l} and D=({f,o,l,l,o,w},` then

Options

A. `AneBneCneD`
B. `AcupBcupCneD`
C. `A=B=CsubD`
D. `A=B=C=D`

Answer

To solve the problem, we need to analyze the given sets and determine their relationships. Let's go through the steps systematically.

### Step-by-Step Solution:

1. **Identify the Sets**:
- Set A = {w, o, l, f}
- Set B = {f, l, o, w}
- Set C = {f, o, w, l}
- Set D = {f, o, l, l, o, w}

2. **Remove Duplicates in Set D**:
- Set D has duplicates (l and o appear twice). In set theory, we only consider distinct elements.
- Therefore, Set D can be simplified to:
- Set D = {f, o, l, w}

3. **Rearranging Elements**:
- In set theory, the order of elements does not matter. We can rearrange the elements in any order.
- Thus, we can write:
- Set A = {w, o, l, f} = {f, o, l, w} (rearranged)
- Set B = {f, l, o, w} = {f, o, l, w} (rearranged)
- Set C = {f, o, w, l} = {f, o, l, w} (rearranged)
- Set D = {f, o, l, w} (after removing duplicates)

4. **Compare the Sets**:
- Now we can see that:
- Set A = {f, o, l, w}
- Set B = {f, o, l, w}
- Set C = {f, o, l, w}
- Set D = {f, o, l, w}
- Therefore, all sets A, B, C, and D are equal.

5. **Conclusion**:
- Since all sets are equal, we conclude that:
- A = B = C = D

### Final Answer:
The correct option is **Option 4: A = B = C = D**.

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