Let's approach each question one by one to list all the elements in the given sets:
(i) Set [tex]\( A \)[/tex]: Odd natural numbers
We are tasked with listing all the odd natural numbers. Here, I'll assume a specific range, say natural numbers less than 100, to make the set finite and practical for our listing purposes.
[tex]\[ A = \{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99\} \][/tex]
(ii) Set [tex]\( B \)[/tex]: Integers between [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{9}{2}\)[/tex]
This set includes all integers that lie between [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{9}{2}\)[/tex].
[tex]\[ B = \{1, 2, 3\} \][/tex]
(iii) Set [tex]\( C \)[/tex]: Integers [tex]\( x \)[/tex] such that [tex]\( x^2 < 4 \)[/tex]
We need to find all integers [tex]\( x \)[/tex] that satisfy the inequality [tex]\( x^2 < 4 \)[/tex]. The integers that lie within this range are those for which absolute value is less than 2, i.e., [tex]\( -2 < x < 2 \)[/tex].
[tex]\[ C = \{-1, 0, 1\} \][/tex]
(iv) Set [tex]\( D \)[/tex]: Letters in the word "ROYAL"
We need to extract all distinct letters in the word "ROYAL".
[tex]\[ D = \{ 'R', 'O', 'Y', 'A', 'L' \} \][/tex]
(v) Set [tex]\( E \)[/tex]: Months of the year that do not have 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), and November (30 days).
[tex]\[ E = \{ "February", "April", "June", "September", "November" \} \][/tex]
(vi) Set [tex]\( F \)[/tex]: Consonants in the English alphabet which precede 'k'
The consonants preceding the letter 'k' in the English alphabet are b, c, d, f, g, h, and j.
[tex]\[ F = \{ 'b', 'c', 'd', 'f', 'g', 'h', 'j' \} \][/tex]
Here we have listed the elements of each set in a clear and detailed manner.
