If `A sub B`, then `A cup B = ?`

Options

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

Answer

To solve the problem, we need to determine the union of two sets A and B given that A is a subset of B.

### Step-by-Step Solution:

1. **Understanding the Definition of Subset**:
- A is a subset of B (denoted as \( A \subseteq B \)) means that every element in set A is also an element of set B. In other words, all elements of A are contained within B.

2. **Definition of Union**:
- The union of two sets A and B (denoted as \( A \cup B \)) is the set that contains all the elements from both sets without any duplicates.

3. **Applying the Definition**:
- Since all elements of A are already included in B, when we take the union of A and B, we are essentially combining the elements of A with those of B. However, since A's elements are already in B, we do not need to add them again.

4. **Conclusion**:
- Therefore, the union \( A \cup B \) will simply be equal to B, because B already contains all the elements of A.
- Mathematically, we can write this as:
\[ A \cup B = B \]

### Final Answer:
\[ A \cup B = B \]