Find all the subsets of each of the following sets :
(i) A={5,7}, (ii) B={a,b,c}
(iii) `C={x, x in W, x le 2}`, (iv) {p:p is a letter in the word 'poor'}

Answer

To find all the subsets of the given sets, we will follow a systematic approach. Let's break down each part step by step.

### (i) Set A = {5, 7}

1. **Identify the elements**: The set A has two elements: 5 and 7.
2. **Calculate the number of subsets**: The number of subsets of a set with n elements is given by \(2^n\). Here, \(n = 2\), so the number of subsets is \(2^2 = 4\).
3. **List the subsets**:
- The empty set: {}
- Subset with one element: {5}, {7}
- Subset with both elements: {5, 7}

Therefore, the subsets of A are:
- {}, {5}, {7}, {5, 7}

### (ii) Set B = {a, b, c}

1. **Identify the elements**: The set B has three elements: a, b, and c.
2. **Calculate the number of subsets**: Here, \(n = 3\), so the number of subsets is \(2^3 = 8\).
3. **List the subsets**:
- The empty set: {}
- Subsets with one element: {a}, {b}, {c}
- Subsets with two elements: {a, b}, {a, c}, {b, c}
- Subset with all elements: {a, b, c}

Therefore, the subsets of B are:
- {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}

### (iii) Set C = {x | x ∈ W, x ≤ 2}

1. **Identify the elements**: Here, W represents the set of whole numbers. The whole numbers less than or equal to 2 are: 0, 1, 2.
2. **List the elements**: So, C = {0, 1, 2}.
3. **Calculate the number of subsets**: Here, \(n = 3\), so the number of subsets is \(2^3 = 8\).
4. **List the subsets**:
- The empty set: {}
- Subsets with one element: {0}, {1}, {2}
- Subsets with two elements: {0, 1}, {0, 2}, {1, 2}
- Subset with all elements: {0, 1, 2}

Therefore, the subsets of C are:
- {}, {0}, {1}, {2}, {0, 1}, {0, 2}, {1, 2}, {0, 1, 2}

### (iv) Set D = {p | p is a letter in the word 'poor'}

1. **Identify the unique letters**: The word 'poor' has the letters: p, o, r. Note that 'o' appears twice, but we only consider unique elements in a set.
2. **List the elements**: So, D = {p, o, r}.
3. **Calculate the number of subsets**: Here, \(n = 3\), so the number of subsets is \(2^3 = 8\).
4. **List the subsets**:
- The empty set: {}
- Subsets with one element: {p}, {o}, {r}
- Subsets with two elements: {p, o}, {p, r}, {o, r}
- Subset with all elements: {p, o, r}

Therefore, the subsets of D are:
- {}, {p}, {o}, {r}, {p, o}, {p, r}, {o, r}, {p, o, r}

### Summary of Subsets:
- Subsets of A: {}, {5}, {7}, {5, 7}
- Subsets of B: {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}
- Subsets of C: {}, {0}, {1}, {2}, {0, 1}, {0, 2}, {1, 2}, {0, 1, 2}
- Subsets of D: {}, {p}, {o}, {r}, {p, o}, {p, r}, {o, r}, {p, o, r}