If `X-Y=Y-X`, the X and Y are _________ sets.
(equal/equivalent)

Answer

To solve the question "If `X - Y = Y - X`, the X and Y are _________ sets", we will analyze the equation step by step.

### Step-by-Step Solution:

1. **Understanding the Equation**:
We start with the equation given in the question:
\[ X - Y = Y - X \]
This means that the elements that are in set X but not in set Y are the same as the elements that are in set Y but not in set X.

2. **Rearranging the Equation**:
We can rearrange the equation to see what it implies about the sets.
\[ X - Y + Y - X = 0 \]
This simplifies to:
\[ (X - Y) + (Y - X) = 0 \]

3. **Analyzing the Result**:
The expression \(X - Y\) represents the elements in X that are not in Y, and \(Y - X\) represents the elements in Y that are not in X. If these two are equal, it implies that there are no unique elements in either set.

4. **Conclusion**:
The only way for \(X - Y\) to equal \(Y - X\) is if both sets contain exactly the same elements. Therefore, we conclude that:
\[ X = Y \]
Hence, X and Y are **equal sets**.

### Final Answer:
The X and Y are **equal** sets.

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