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, 1/2 < x < 9/2}

(iii) C = {x : x is an integer, $x^2\le 4$}

(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 precedes K}

Answer 1

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

$\therefore$ A = {1, 3, 5, 7,............}

(ii) B = {x : x is an integer, -1/2 < x < 9/2}

$\therefore$ B = {0, 1, 2, 3, 4}

(iii) C = {x : x is an integer, $x^2\le 4$}

$\therefore x^2\le 4\Rightarrow x\le \pm 2\Rightarrow -2\le x\le 2$

$\therefore$ C = {-2, -1, 0, 1, 2}

(iv) D = {x : x is a letter in the word "LOYAL"}

$\therefore$ D = {L, O, Y, A}

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

$\therefore$ E = {February, April, June, September, November}

(vi) F = {x : x is a consonant in the English alphabet which precedes K}

$\therefore$ F = {B, C, D, F, G, H, J}