Suppose A and B are two sets such that `A cap B =A` and `A = B = phi` , then

Options

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

Answer

To solve the problem, we need to analyze the given conditions step by step.

### Step 1: Understand the Given Conditions
We are given two sets, A and B, with the following conditions:
1. \( A \cap B = A \)
2. \( A = B = \phi \) (where \( \phi \) represents the empty set)

### Step 2: Analyze the Condition \( A \cap B = A \)
The intersection of sets A and B, denoted as \( A \cap B \), is defined as the set of elements that are common to both A and B. The condition \( A \cap B = A \) implies that every element of A is also an element of B.

### Step 3: Substitute the Values of A and B
Since we have \( A = B = \phi \), we can substitute these values into the intersection condition:
- \( A \cap B = \phi \cap \phi = \phi \)

### Step 4: Verify the Condition
Now we check if the condition \( A \cap B = A \) holds true:
- We have \( \phi = A \)
- Thus, \( \phi = A \) is satisfied since both sides are equal.

### Step 5: Conclude the Relationship Between A and B
Since both sets A and B are equal to the empty set, we conclude:
- \( A = B = \phi \)

### Final Conclusion
The conclusion we can draw from the given conditions is that both sets A and B are empty sets. Therefore, the answer is:
- \( A = B = \phi \)