In rule method the null set is represented by

- A
$\{\}$

- B
$\phi $

- C
$\{ x:x = x\} $

- D
$\{ x:x \ne x\} $

Let $S = \{ 0,\,1,\,5,\,4,\,7\} $. Then the total number of subsets of $S$ is

Are the following pair of sets equal ? Give reasons.

$A = \{ 2,3\} ,\quad \,\,\,B = \{ x:x$ is solution of ${x^2} + 5x + 6 = 0\} $

$A = \{ x:x \ne x\} $ represents

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 are sets ? Justify your answer.

The collection of all even integers.