If A =P[1, 2], where P denotes the power set, then which one of the following is correct?

Options

A. `{1,2} sub A`
B. `1 in A`
C. `phi in A`
D. `{1,2} in A`

Answer

To solve the problem, we need to understand what the power set of a set is and then analyze the options given in the question.

### Step-by-Step Solution:

1. **Define the Set**:
We are given the set \( S = \{1, 2\} \).

2. **Find the Power Set**:
The power set \( P(S) \) is the set of all subsets of \( S \). The subsets of \( S = \{1, 2\} \) are:
- The empty set: \( \emptyset \)
- The singleton sets: \( \{1\} \) and \( \{2\} \)
- The set itself: \( \{1, 2\} \)

Therefore, the power set \( P(S) \) is:
\[ P(S) = \{\emptyset, \{1\}, \{2\}, \{1, 2\}\} \]

3. **Identify Set A**:
From the problem, we have \( A = P(S) = \{\emptyset, \{1\}, \{2\}, \{1, 2\}\} \).

4. **Analyze Each Option**:
- **Option A**: \( \{1, 2\} \subseteq A \)
- This is incorrect because \( \{1, 2\} \) is an element of \( A \) but not a subset of \( A \).
- **Option B**: \( 1 \in A \)
- This is incorrect because \( 1 \) is not an element of \( A \).
- **Option C**: \( \emptyset \in A \)
- This is correct because the empty set \( \emptyset \) is indeed an element of \( A \).
- **Option D**: \( \{1, 2\} \in A \)
- This is correct because \( \{1, 2\} \) is an element of \( A \).

5. **Conclusion**:
The correct options are C and D.

### Final Answer:
- The correct options are C: \( \emptyset \in A \) and D: \( \{1, 2\} \in A \).