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

(ii) B = {x: x is an integer;}

It can be seen that and

∴ B

(iii) C = {x: x is an integer;}

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}