List all the elements of the following sets:

(i) A = {xx is an odd natural number}

(ii) B = {xx is an integer, \( -\dfrac{1}{2}\) < x < \( \dfrac{9}{2}\)}

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

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

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

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

Asked by Abhisek | 11 months ago |  70

1 Answer

Solution :-

(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, \( -\dfrac{1}{2}\) < x < \( \dfrac{9}{2}\)}

We know that \( -\dfrac{1}{2}\) = – 0.5 and \( \dfrac{9}{2}\) = 4.5

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

 

(iii) C = {x: x is an integer, x2 ≤ 4}

We know that

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

Here

02 = 0 ≤ 4, 12 = 1 ≤ 4, 22 = 4 ≤ 4, 32 = 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}

Answered by Abhisek | 11 months ago

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