If `PsubeQ` and `QsubeP`, then ______.

Answer

To solve the question, we need to analyze the relationship between the sets P and Q based on the given conditions.

### Step-by-Step Solution:

1. **Understanding Subsets**:
- A set A is a subset of set B (denoted as A ⊆ B) if every element of A is also an element of B.

2. **Given Conditions**:
- We have two conditions:
- \( P \subseteq Q \) (P is a subset of Q)
- \( Q \subseteq P \) (Q is a subset of P)

3. **Implications of the Conditions**:
- From \( P \subseteq Q \), we know that every element in P is also in Q.
- From \( Q \subseteq P \), we know that every element in Q is also in P.

4. **Conclusion**:
- Since all elements of P are in Q and all elements of Q are in P, it follows that both sets contain exactly the same elements.
- Therefore, we can conclude that \( P = Q \).

### Final Answer:
If \( P \subseteq Q \) and \( Q \subseteq P \), then \( P = Q \).

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