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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, } (iii) C = { x : x is an 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 }.

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Solution

## (i) Given, x is an odd number. Thus, the elements of set A are 1,3,5,7,9,11,.... Therefore, A={ 1,3,5,7,9,11,.... } (ii) Given −1 2 <x< 9 2 . Therefore, x lies between −0.5 and 4.5 Further, x is an integer. Therefore, integers lying between -0.5 and 4.5 are 0, 1, 2, 3, 4 Thus, B={ 0,1,2,3,4 } . (iii) Given, x 2 ≤4 , where x is an integer. Solving for x, x 2 ≤4 x=±2 −2≤x≤2 Also, x is an integer. Therefore, the elements of set C are integers between −2 and +2 . Hence, C={ −2,−1,0,1,2 } . (iv) Given, x is a letter in the word “LOYAL”. Letter L is repeated in the word “LOYAL”. Thus, the unique elements of the word LOYAL are A, L, O and Y. Thus, D={ A,L,O,Y } . (v) Given x is a month of the year that does not have 31 days. The months with less than 31 days are February, April, June, September, and November. Therefore, E={ February, April, June, September and November } . (vi) Given, x is a consonant which precedes k. The consonants before letter k are b, c, d, f, g, h, j. Thus, F={ b, c, d, f, g, h, j }

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