Question

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 < x < 9/2}
(iii) C = {x: x is an integer, x2 ≤ 4}
(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}.
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Answer 1

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

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

(ii) B = {x: x is an integer, -1/2 < x < 9/2}

We know that – 1/2 = – 0.5 and 9/2 = 4.5

So the elements are B = {0, 1, 2, 3, 4}.

(iii) C = {x: x is an integer, x^2 ≤ 4}

We know that

(–1)^2 = 1 ≤ 4; (–2)^2 = 4 ≤ 4; (–3)^2 = 9 > 4

Here

0^2 = 0 ≤ 4, 1^2 = 1 ≤ 4, 2^2 = 4 ≤ 4, 3^2 = 9 > 4

So we get

C = {–2, –1, 0, 1, 2}

(iv) D = {x: x is a letter in the word “LOYAL”}

So the elements are D = {L, O, Y, A}

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

So the elements are E = {February, April, June, September, November}

(vi) F = {x: x is a consonant in the English alphabet which proceeds k}

So the elements are F = {b, c, d, f, g, h, j}

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Answer 2

Answer:

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

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

(ii) B = {x: x is an integer, -1/2 < x < 9/2}

We know that – 1/2 = – 0.5 and 9/2 = 4.5

So the elements are B = {0, 1, 2, 3, 4}.

(iii) C = {x: x is an integer, x^2 ≤ 4}

We know that

(–1)^2 = 1 ≤ 4; (–2)^2 = 4 ≤ 4; (–3)^2 = 9 > 4

Here

0^2 = 0 ≤ 4, 1^2 = 1 ≤ 4, 2^2 = 4 ≤ 4, 3^2 = 9 > 4

So we get

C = {–2, –1, 0, 1, 2}

(iv) D = {x: x is a letter in the word “LOYAL”}

So the elements are D = {L, O, Y, A}

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

So the elements are E = {February, April, June, September, November}

(vi) F = {x: x is a consonant in the English alphabet which proceeds k}

So the elements are F = {b, c, d, f, g, h, j}

Step-by-step explanation:

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