Write the power set of each of the set (i) `{a,b}`, (ii) `{a,b,c}`.

Answer

To find the power set of a given set, we need to identify all possible subsets of that set, including the empty set and the set itself. Let's solve the problem step by step for both parts.

### Part (i): Power Set of the Set `{a, b}`

1. **Identify the Set**: The given set is `{a, b}`.
2. **Find All Subsets**:
- The empty set: `{}`
- Subset with one element: `{a}`
- Subset with one element: `{b}`
- Subset with both elements: `{a, b}`
3. **List All Subsets**: The subsets we found are:
- `{}`
- `{a}`
- `{b}`
- `{a, b}`
4. **Form the Power Set**: The power set is the set of all subsets:
- Power set: `{{}, {a}, {b}, {a, b}}`

### Part (ii): Power Set of the Set `{a, b, c}`

1. **Identify the Set**: The given set is `{a, b, c}`.
2. **Find All Subsets**:
- The empty set: `{}`
- Subsets with one element: `{a}`, `{b}`, `{c}`
- Subsets with two elements: `{a, b}`, `{a, c}`, `{b, c}`
- Subset with all three elements: `{a, b, c}`
3. **List All Subsets**: The subsets we found are:
- `{}`
- `{a}`
- `{b}`
- `{c}`
- `{a, b}`
- `{a, c}`
- `{b, c}`
- `{a, b, c}`
4. **Form the Power Set**: The power set is the set of all subsets:
- Power set: `{{}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}`

### Final Answer:
- Power set of `{a, b}`: `{{}, {a}, {b}, {a, b}}`
- Power set of `{a, b, c}`: `{{}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}`