Write of the following sets in the set builder from :
`{:((i),{1},(ii),{-1","1}),((iii),{1","7","49","343},(iv),{0","5","10","15","....}):}`
`(v) {B,E,N,G,I}" "(vi){14,21,28,35,42,....,98}`
`(v) {1,0}" "(vi){1,3,5,7,9}`

Answer

To write the given sets in set builder form, we will analyze each set and express the elements in a mathematical notation that describes the properties of the elements.

### Step-by-Step Solution:

1. **Set (i): {1, -1}**
- The elements of this set are the solutions to the equation \( x^2 = 1 \).
- Therefore, we can express this set in set builder form as:
\[ S_1 = \{ x \mid x^2 = 1 \} \]

2. **Set (ii): {1, 7, 49, 343}**
- These numbers can be expressed as powers of 7: \( 7^0, 7^1, 7^2, 7^3 \).
- Thus, we can write this set as:
\[ S_2 = \{ x \mid x = 7^n, n \in \{0, 1, 2, 3\} \} \]

3. **Set (iii): {0, 5, 10, 15, ...}**
- This set consists of multiples of 5, starting from 0.
- We can express this set in set builder form as:
\[ S_3 = \{ x \mid x = 5n, n \in \mathbb{W} \} \]
where \(\mathbb{W}\) denotes the set of whole numbers (0, 1, 2, ...).

4. **Set (iv): {B, E, N, G, I}**
- This set contains the letters of the word "BENGI".
- We can express this set as:
\[ S_4 = \{ x \mid x \text{ is a letter in the word "BENGI"} \} \]

5. **Set (v): {14, 21, 28, 35, 42, ..., 98}**
- These numbers are multiples of 7, starting from 14 up to 98.
- We can express this set in set builder form as:
\[ S_5 = \{ x \mid x = 7n, n \in \mathbb{N}, n \leq 14 \} \]

6. **Set (vi): {1, 0}**
- The elements of this set are the solutions to the equation \( x(x - 1) = 0 \).
- Therefore, we can express this set in set builder form as:
\[ S_6 = \{ x \mid x(x - 1) = 0 \} \]

7. **Set (vii): {1, 3, 5, 7, 9}**
- This set consists of odd numbers less than 10.
- We can express this set in set builder form as:
\[ S_7 = \{ x \mid x \text{ is an odd number and } x < 10 \} \]

### Final Set Builder Forms:
1. \( S_1 = \{ x \mid x^2 = 1 \} \)
2. \( S_2 = \{ x \mid x = 7^n, n \in \{0, 1, 2, 3\} \} \)
3. \( S_3 = \{ x \mid x = 5n, n \in \mathbb{W} \} \)
4. \( S_4 = \{ x \mid x \text{ is a letter in the word "BENGI"} \} \)
5. \( S_5 = \{ x \mid x = 7n, n \in \mathbb{N}, n \leq 14 \} \)
6. \( S_6 = \{ x \mid x(x - 1) = 0 \} \)
7. \( S_7 = \{ x \mid x \text{ is an odd number and } x < 10 \} \)