Write the power set of the following :
(i) {1,2}
(ii) {1,2,3}.

Answer

To find the power set of a given set, we need to list all possible subsets of that set, including the empty set and the set itself. Let's solve the question step by step.

### (i) Power Set of {1, 2}

1. **Identify the set**: The given set is {1, 2}.

2. **List all subsets**:
- The empty set: ∅
- Subset with one element: {1}, {2}
- Subset with both elements: {1, 2}

3. **Combine all subsets**:
- The power set is the collection of all these subsets.
- Therefore, the power set of {1, 2} is:
\[ P({1, 2}) = \{\emptyset, \{1\}, \{2\}, \{1, 2\}\} \]

### (ii) Power Set of {1, 2, 3}

1. **Identify the set**: The given set is {1, 2, 3}.

2. **List all subsets**:
- The empty set: ∅
- Subsets with one element: {1}, {2}, {3}
- Subsets with two elements: {1, 2}, {1, 3}, {2, 3}
- Subset with all elements: {1, 2, 3}

3. **Combine all subsets**:
- The power set is the collection of all these subsets.
- Therefore, the power set of {1, 2, 3} is:
\[ P({1, 2, 3}) = \{\emptyset, \{1\}, \{2\}, \{3\}, \{1, 2\}, \{1, 3\}, \{2, 3\}, \{1, 2, 3\}\} \]

### Final Answers:
- Power set of {1, 2} is:
\[ P({1, 2}) = \{\emptyset, \{1\}, \{2\}, \{1, 2\}\} \]

- Power set of {1, 2, 3} is:
\[ P({1, 2, 3}) = \{\emptyset, \{1\}, \{2\}, \{3\}, \{1, 2\}, \{1, 3\}, \{2, 3\}, \{1, 2, 3\}\} \]