Question

List all the elements of the following sets: 
(i) A = {x: x is an odd natural number} 
(ii) B = {x: x is an \(\frac{-1}{2} < x <\frac{ 9}{2}\)  integer,} 
(iii) C = {x: x is an \(x^2 ≤ 4 \) integer, 
(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 proceeds k}.

Answer 1

(i) A = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}

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(ii) B = {x: x\(\frac{ -1}{2} < n < \frac{9}{2}\) is an integer.
it can be seen \(\frac{-1}{2} = -0.5\)  and \(\frac{9}{2}=4.5\) that
∴  B= {0,1,2,3,4}

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(iii) C = {x: x is an integer. \(x^2 ≤ 4\) it can be seen that 
\((-1)^2 = 1 ≤ 4; (-2)^2 = 4 ≤ 4; (-3)^2\)
\(= 9 > 4\)
\(0^2 = 0 ≤ 4\)
\(1^2 = 1 ≤ 4\)
\(2^2 = 4 ≤ 4\)
\(3^2= 9 > 4\)
∴C = {-2, -1, 0, 1, 2}

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(iv) D = (x: x is a letter in the word “LOYAL“) = {L, O, Y, A}

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(v) E = {x: x is a month of a year not having 31 days}
= {February, April, June, September, November}

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(vi) F = {x: x is a consonant in the English alphabet which precedes k}
= {b, c, d, f, g, h, j}