If A and B are two events such that
`P(A) ne0` and `P(B//A)=1,` then :

Options

A. `A sub B`
B. `B sub A`
C. `B = phi`
D. `A=phi`

Answer

To solve the problem, we need to analyze the given information about the events A and B.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We know that \( P(A) \neq 0 \). This means that event A has a non-zero probability of occurring.
- We are also given that \( P(B|A) = 1 \). This indicates that if event A occurs, then event B definitely occurs.

2. **Using the Definition of Conditional Probability**:
- The conditional probability \( P(B|A) \) is defined as:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]
- Since \( P(B|A) = 1 \), we can set up the equation:
\[ 1 = \frac{P(A \cap B)}{P(A)} \]

3. **Rearranging the Equation**:
- From the equation above, we can multiply both sides by \( P(A) \) (which is non-zero):
\[ P(A \cap B) = P(A) \]

4. **Interpreting the Result**:
- The equation \( P(A \cap B) = P(A) \) tells us that the probability of both A and B occurring is equal to the probability of A occurring. This implies that whenever A occurs, B must also occur.
- Therefore, we can conclude that event A is a subset of event B, denoted as:
\[ A \subseteq B \]

5. **Conclusion**:
- Since A is a subset of B, we can say that if A occurs, B will definitely occur, which is consistent with the given information \( P(B|A) = 1 \).

### Final Answer:
Thus, the relationship between events A and B is:
\[ A \subseteq B \]