If A and B are two sets such that `AsubB` , then what is `AuuB`?

Answer

To solve the problem, we need to determine what \( A \cup B \) is given that \( A \subseteq B \).

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We know that \( A \subseteq B \). This means that every element of set \( A \) is also an element of set \( B \).

**Hint**: Remember that a subset means all elements of the first set are contained within the second set.

2. **Definition of Union**:
The union of two sets \( A \) and \( B \), denoted as \( A \cup B \), is the set that contains all elements that are in \( A \), in \( B \), or in both.

**Hint**: The union combines all unique elements from both sets.

3. **Applying the Definition**:
Since all elements of \( A \) are already included in \( B \), when we take the union \( A \cup B \), we are essentially combining the elements of \( A \) with those of \( B \). However, since \( A \) is a subset of \( B \), the union will not add any new elements beyond those already in \( B \).

**Hint**: Visualize this with a Venn diagram where \( A \) is inside \( B \).

4. **Conclusion**:
Therefore, \( A \cup B = B \).

**Final Answer**: \( A \cup B = B \)