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 }.

Answer 1

(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 }