Write the following sets in Set - Builder Form :
(a) (i) A={0}
(ii) B={-1,1}
(iii) C={1,3,5,7,9}
(iv) D={2,4,6,8}
(v) E={1,5,10,15,……}
(vi) F= {12,18,24,…,96}.
(b) (i) ,6,9,12}
(iii) {2,4,8,16,32}
(iii) {5,25,125,625}
(iv) {2,4,6,....}
(v) {1,4,9,.....100}

Answer

To express the given sets in set-builder form, we will define a rule that describes the elements of each set. Here’s the step-by-step solution:

### Step 1: Set A = {0}
- **Set-builder form**: A = {x | x = 0}

### Step 2: Set B = {-1, 1}
- **Set-builder form**: B = {x | x² = 1}

### Step 3: Set C = {1, 3, 5, 7, 9}
- **Set-builder form**: C = {x | x = 2k - 1, k ∈ {1, 2, 3, 4, 5}}

### Step 4: Set D = {2, 4, 6, 8}
- **Set-builder form**: D = {x | x = 2k, k ∈ {1, 2, 3, 4}}

### Step 5: Set E = {1, 5, 10, 15, ...}
- **Set-builder form**: E = {x | x = 5k, k ∈ ℕ} ∪ {1}

### Step 6: Set F = {12, 18, 24, ..., 96}
- **Set-builder form**: F = {x | x = 6k, k ∈ {2, 3, 4, ..., 16}}

### Step 7: Set G = {6, 9, 12}
- **Set-builder form**: G = {x | x = 3k, k ∈ {2, 3, 4}}

### Step 8: Set H = {2, 4, 8, 16, 32}
- **Set-builder form**: H = {x | x = 2^k, k ∈ {1, 2, 3, 4, 5}}

### Step 9: Set I = {5, 25, 125, 625}
- **Set-builder form**: I = {x | x = 5^k, k ∈ {1, 2, 3, 4}}

### Step 10: Set J = {2, 4, 6, ...}
- **Set-builder form**: J = {x | x = 2k, k ∈ ℕ}

### Step 11: Set K = {1, 4, 9, ..., 100}
- **Set-builder form**: K = {x | x = k², k ∈ {1, 2, ..., 10}}