Which of the following are sets ? Justify your answer.

A collection of most dangerous animals of the world.

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ x:x$ is an equilateral triangle in a plane $\}  \ldots \{ x:x$ is a triangle in the same plane $\} $

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\varnothing \in A$

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\,\} $

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}\} $

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\} $