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

$(i)$ $\{ P,R,I,N,C,A,L\} $ | $(a)$ $\{ x:x$ is a positive integer and is adivisor of $18\} $ |

$(ii)$ $\{ \,0\,\} $ | $(b)$ $\{ x:x$ is an integer and ${x^2} - 9 = 0\} $ |

$(iii)$ $\{ 1,2,3,6,9,18\} $ | $(c)$ $\{ x:x$ is an integer and $x + 1 = 1\} $ |

$(iv)$ $\{ 3, - 3\} $ | $(d)$ $\{ x:x$ is aletter of the word $PRINCIPAL\} $ |

Since in $(d),$ there are $9$ letters in the word $PRINCIPAL$ and two letters $P$ and $I$ are repeated, so

$(i)$ matches $(d).$ Similarly, $(ii)$ matches $(c)$ as $x+1=1$ implies $x=0 .$ Also, $1,2,3,6,9,18$ are all divisors of $18$ and so $(iii)$ matches $(a).$ Finally, $x^{2}-9=0$ implies $x=3,-3$ and so $(iv)$ matches $(b).$

If $Q = \left\{ {x:x = {1 \over y},\,{\rm{where \,\,}}y \in N} \right\}$, then

Which of the following are sets ? Justify your answer.

A team of eleven best-cricket batsmen of the world.

Which of the following sets are finite or infinite.

The set of prime numbers less than $99$

Write the following intervals in set-builder form :

$\left[ {6,12} \right]$

Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of $m \times n$ is

- [JEE MAIN 2020]