If `A subeB`, then the value of `A cup B ` is

Options

A. A
B. B
C. `phi`
D. None of these

Answer

To solve the problem, we need to understand the relationship between the sets A and B given that \( A \subseteq B \) (A is a subset of B). We want to find the value of \( A \cup B \) (the union of sets A and B).

### Step-by-Step Solution:

1. **Understanding the Definition of Subset**:
- Since \( A \subseteq B \), every element of set A is also an element of set B. This means that all elements in A are contained within B.

**Hint**: Recall that a subset means all elements of one set are found in another set.

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

**Hint**: Union combines all unique elements from both sets.

3. **Applying the Definitions**:
- Since all elements of A are in B, when we take the union \( A \cup B \), we are essentially collecting all elements from both sets. However, since A is already included in B, the union will not add any new elements beyond those already in B.

**Hint**: Think about what happens when you combine a smaller set with a larger set that contains it.

4. **Conclusion**:
- Therefore, the value of \( A \cup B \) is simply equal to set B.

\[ A \cup B = B \]

### Final Answer:
If \( A \subseteq B \), then \( A \cup B = B \).