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}