`AuuB=A`, then :

Options

A. `AsubB`
B. `BsubA`
C. `AcancelsubB` and `BcancelsubA`
D. none of these

Answer

To solve the problem `A ∪ B = A`, we need to analyze what this equation means in terms of set theory.

### Step-by-Step Solution:

1. **Understanding the Union**: The union of two sets A and B, denoted as A ∪ B, is the set that contains all elements that are in A, in B, or in both.

2. **Given Condition**: The equation states that A ∪ B = A. This means that when we combine the elements of sets A and B, we do not get any new elements beyond those already in A.

3. **Implication of the Condition**: For A ∪ B to equal A, it implies that every element of B must already be included in A. If there were any elements in B that were not in A, those elements would appear in the union, making A ∪ B larger than A.

4. **Conclusion About Subsets**: Since all elements of B are contained within A, we can conclude that B is a subset of A. This is denoted as B ⊆ A.

5. **Final Answer**: Therefore, the correct answer to the question is that B is a subset of A.