List all the elements of the following sets :
(i) A= {x:x is an odd natural number}
(ii) B= {x:x is an integer , `-(1)/(2)ltxlt(9)/(2)}`
(iii) `C={x:x^(2)le4,x inZ}`
(iv) D={x:x is a letter in the word LOYAL'}
(v) E= {x:x is a month of a year not having 31 days }
(vi) F= {x:x is a consonant in the English alphabet , which precedes k}.

Answer

To solve the problem of listing the elements of the given sets, we will analyze each set one by one.

### Step-by-Step Solution:

**(i) Set A: A = {x : x is an odd natural number}**

Odd natural numbers start from 1 and continue indefinitely. Therefore, the elements of set A are:
\[ A = \{1, 3, 5, 7, 9, \ldots\} \]

**(ii) Set B: B = {x : x is an integer, \(-\frac{1}{2} < x < \frac{9}{2}\)}**

The integers between \(-\frac{1}{2}\) and \(\frac{9}{2}\) are:
- The smallest integer greater than \(-\frac{1}{2}\) is 0.
- The largest integer less than \(\frac{9}{2} = 4.5\) is 4.

Thus, the elements of set B are:
\[ B = \{0, 1, 2, 3, 4\} \]

**(iii) Set C: C = {x : \(x^2 \leq 4\), x in Z}**

We need to find integers \(x\) such that \(x^2\) is less than or equal to 4. The possible values of \(x\) are:
- From \(x^2 \leq 4\), we have \(-2 \leq x \leq 2\).
- Therefore, the integers are \(-2, -1, 0, 1, 2\).

Thus, the elements of set C are:
\[ C = \{-2, -1, 0, 1, 2\} \]

**(iv) Set D: D = {x : x is a letter in the word 'LOYAL'}**

The letters in the word 'LOYAL' are L, O, Y, A. However, we need to list each letter only once. Thus, the elements of set D are:
\[ D = \{L, O, Y, A\} \]

**(v) Set E: E = {x : x is a month of a year not having 31 days}**

The months that do not have 31 days are:
- February (28 or 29 days)
- April (30 days)
- June (30 days)
- September (30 days)
- November (30 days)

Thus, the elements of set E are:
\[ E = \{February, April, June, September, November\} \]

**(vi) Set F: F = {x : x is a consonant in the English alphabet, which precedes K}**

The consonants that precede K in the English alphabet are:
- B, C, D, F, G, H, J

Thus, the elements of set F are:
\[ F = \{B, C, D, F, G, H, J\} \]

### Final Summary of Sets:
- \( A = \{1, 3, 5, 7, 9, \ldots\} \)
- \( B = \{0, 1, 2, 3, 4\} \)
- \( C = \{-2, -1, 0, 1, 2\} \)
- \( D = \{L, O, Y, A\} \)
- \( E = \{February, April, June, September, November\} \)
- \( F = \{B, C, D, F, G, H, J\} \)