Question 5:

List all the elements of the following sets :

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

(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}.

Answer

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

 

It can be seen that −1/2 = 0.5 and 9/2 = 4.5

It can be seen that

∴ B ={0, 1, 2, 3, 4}

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

It can be seen that

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

0² = 0 ≤ 4

1² = 1 ≤ 4

2² = 4 ≤ 4

3² = 9 > 4

∴C = {−2, −1, 0, 1, 2}

(iv) D = (x: x is a letter in the word “LOYAL”) = {L, O, Y, A}

(v) E = {x: x is a month of a year not having 31 days} = {February, April, June, September, November}

(vi) F = {x: x is a consonant in the English alphabet which precedes k} = {b, c, d, f, g, h, j }

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