Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

$(i)$ $\{1,2,3,6\}$ | $(a)$ $\{ x:x$ is a prime number and a divisor $6\} $ |

$(ii)$ $\{2,3\}$ | $(b)$ $\{ x:x$ is an odd natural number less than $10\} $ |

$(iii)$ $\{ M , A , T , H , E , I , C , S \}$ | $(c)$ $\{ x:x$ is natural number and divisor of $6\} $ |

$(iv)$ $\{1,3,5,7,9\}$ | $(d)$ $\{ x:x$ a letter of the work $\mathrm{MATHEMATICS}\} $ |

$(i)$ All the elements of this set are natural numbers as well as the divisors of $6 .$ Therefore, $(i)$ matches with $(c).$

$(ii)$ It can be seen that $2$ and $3$ are prime numbers. They are also the divisors of $6 .$ Therefore, $(ii)$ matches with $(a).$

$(iii)$ All the elements of this set are letters of the word $MATHEMATICS.$ Therefore, $(iii)$ matches with $(d).$

$(iv)$ All the elements of this set are odd natural numbers less than $10 .$ Therefore, $(iv)$ matches with $(b).$

Write down all the subsets of the following sets

$\emptyset $

List all the elements of the following sers :

$A = \{ x:x$ is an odd natural number $\} $

Find the pairs of equal sets, if any, give reasons:

$A = \{ 0\} ,$

$B = \{ x:x\, > \,15$ and $x\, < \,5\} $

$C = \{ x:x - 5 = 0\} ,$

$D = \left\{ {x:{x^2} = 25} \right\}$

$E = \{ \,x:x$ is an integral positive root of the equation ${x^2} - 2x - 15 = 0\,\} $

Which of the following are sets ? Justify your answer.

The collection of all the months of a year beginning with the letter $\mathrm{J}.$

Write the following sets in roster form :

$C = \{ x:x{\rm{ }}$ is a two-digit natural number such that sum of its digits is $8\} $