List all the elements of the following sets:

Solution:

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

(ii) $\mathrm{B}=\left\{x: x\right.$ is an integer; $\left.-\frac{1}{2}

It can be seen that $-\frac{1}{2}=-0.5$ and $\frac{9}{2}=4.5$

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

(iii) $C=\left\{x: x\right.$ is an integer; $\left.x^{2} \leq 4\right\}$

It can be seen that

$(-1)^{2}=1 \leq 4 ;(-2)^{2}=4 \leq 4 ;(-3)^{2}=9>4$

$0^{2}=0 \leq 4$

$1^{2}=1 \leq 4$

$2^{2}=4 \leq 4$

$3^{2}=9>4$

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

(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 $k\}$

$=\{b, c, d, f, g, h, j\}$