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\} $ |

Which of the following is the empty set

Write down all the subsets of the following sets

$\{ a\} $

Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to

- [IIT 2010]

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $x$ is prime $\} $