Question

List all the elements of the following sets:
(i) $A=\{x:x\text{is an odd natural number}\}$
(ii) $B=\{x:x\text{is an integer},\frac{-1}{2}<x<\frac{9}{2}\}$
(iii) $C=\{x:x\text{is an integer},x^2\le 4\}$
(iv) $D=\{x:x\text{is a letter in the word LOYAL}\}$
(v) $E=\{x:x\text{is a month of a year not having 31 days}\}$
(vi) $F=\{x:x\text{is a consonant in the English alphabet which precedes k}\}$

Answer 1

(i) $A=\{x:x\text{is an odd natural number}\}=\{1,3,5,7,9.....\}$
(ii) $B=\{x:x\text{is an integer},-\frac{1}{2}<x<\frac{9}{2}\}$
Since, $-\frac{1}{2}=-0.5$ and $\frac{9}{2}=4.5$
$\therefore B=\{0,1,2,3,4\}$
(iii) $C=\{x:x\text{is an integer};x^2\le 4\}$
It can be seen that
$(-1{)}^2=1\le 4$
$;(-2{)}^2=4\le 4$
$;(-3{)}^2=9>4$
$0^2=0\le 4$
$1^2=1\le 4$
$2^2=4\le 4$
$3^2=9>4$
$\therefore C=\{-2,-1,0,1,2\}$
(iv) $D=\{x:x\text{is a letter in the word LOYAL}\}=\{L,O,Y,A\}$
(v) $E=\{x:x\text{is a month of a year not having 31 days}\}$
$=\left\{\text{February, April, June, September, November}\right\}$
(vi) $F=\{x:x\text{is a consonant in the English alphabet which precedes k}\}=\{b,c,d,f,g,h,j\}$