Q. Which of the following sets are finite or infinite
(i) The set of months of a year
(ii) $\{1,2,3,....\}$
(iii) $\{1,2,3,....99,100\}$
(iv) The set of positive integers greater than $100$
(v) The set of prime numbers less than $99$

Q. State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of $5$
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0, 0)

Q. Which of the following are examples of the null set?
(i) Set of odd natural numbers divisible by $$2$$
(ii) Set of even prime numbers
(iii) $$\left \{ x : x \text { is a natural numbers, $$x < 5$$ and $$x > 7}\right \}$$
(iv) $$\left \{ y : y \text { is a point common to any two parallel lines}\right \}$$

Q. Let $A=\{1,2,3,4,5,6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
(i) 5. . .A (ii) 8 . . . A (iii) 0. . .A (iv) 4. . . A (v) 2. . .A (vi) 10. . .A

Q. Write the following sets in roster form:
(i) $A=\{x:x\text{is an integer and}-3<x<7\}$
(ii) $B=\{x:x\text{is a natural number less than 6}\}$
(iii) $C=\{x:x\text{is a two-digit natural number such that the sum of its digits is 8}\}$
(iv) $D=\{x:x\text{is a prime number which is divisor of 60}\}$
(v) $E=$ The set of all letters in the word TRIGONOMETRY
(vi) $F=$ The set of all letters in the word BETTER

Q. 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) $\{x:x\text{is a prime number and a divisor of 6}\}$
(ii) $\{2,3\}$	(b) $\{x:x\text{is an odd natural number less than 10}\}$
(iii) $\{M,A,T,H,E,I,C,S\}$	(c) $\{x:x\text{is natural number and divisor of 6}\}$
(iv) $\{1,3,5,7,9\}$	(d) $\{x:x\text{is a letter of the word MATHEMATICS}\}$

Q. In the following, state whether $A=B$ or not:
(i) $A=\{a,b,c,d\}B=\{d,c,b,a\}$
(ii) $A=\{4,8,12,16\}B=\{8,4,16,18\}$
(iii) $A=\{2,4,6,8,10\}B=\{x:x\text{is a positive even integer and}x\le 10\}$
(iv) $A=\{x:x\text{is a multiple of 10}\},B=\{10,15,20,25,30,...\}$

Q. How many elements has $P\left(A\right)$ , if $A=\varphi$?

Q. Write the following intervals in set-builder form:
(i) $(-3,0)$

Q. List all the elements of the following sets:
(i) $A=\{x:x\text{is an odd natural number}\}$
(ii) $B=\{x:x\text{is an integer},\frac{-1}{2}<x<\frac{9}{2}\}$
(iii) $C=\{x:x\text{is an integer},x^2\le 4\}$
(iv) $D=\{x:x\text{is a letter in the word LOYAL}\}$
(v) $E=\{x:x\text{is a month of a year not having 31 days}\}$
(vi) $F=\{x:x\text{is a consonant in the English alphabet which precedes k}\}$

Q. Examine whether the following statements are true or false:
(i) { $a,b$ } $\subset ̸$ { $b,c,a$ }
(ii) { $a,e$ } $\subset$ { $x:x$ is a vowel in the English alphabet}
(iii) { $1,2,3$ } $\subset$ { $1,3,5$ }
(iv) { $a$ }$\subset$ { $a,b,c$ }
(v) { $a$ }$ϵ$ { $a,b,c$ }
(vi) { $x:x$ is an even natural number less than $6$} $\subset$ { $x$ : x is a natural number which divides $36$ }

Q. Which of the following are sets ? Justify your answer.
(i) The collection of all the months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than $100.$
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world

Q. Write the following as intervals :
(i) $\{x:xϵR,4<x\le 6\}$

Q. Are the following pair of sets equal ? Give reasons.
(i) $A=\{2,3\},B=\{x:x\text{is solution of}{x}^2+5x+6=0\}$
(ii) $A=\{x:x\text{is a letter in the word FOLLOW}\}$

Q. Make correct statements by filling in the symbols $\subset$ or $\subset ̸$ in blank spaces:
(i) $\{2,3,4\}......\{1,2,3,4,5\}$
(ii) $\{a,b,c\}...\{b,c,d\}$
(iii) {$x:x$ is a student of Class XI of your school}. . .{$x:x$ student of your school}
(iv) {$x:x$ is a circle in the plane} . . .{$x:x$ is a circle in the same plane with radius 1 unit}
(v) {$x:x$ is a triangle in a plane} . . . {$x:x$ is a rectangle in the plane}
(vi) {$x:x$ is an equilateral triangle in a plane} . . . {$x:x$ is a triangle in the same plane}
(vii) {$x:x$ is an even natural number} . . . {$x:x$ is an integer}

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

Q. What universal set(s) would you propose for each of the following:
(i) The set of right triangles. (ii) The set of isosceles triangles

Q. Write the following sets in the set-builder form
(i) $\{3,6,9,12\}$
(ii) $\{2,4,8,16,32\}$
(iii) $\{5,25,125,625\}$
(iv) $\{2,4,6,...\}$
(v) $\{1,4,9,...,100\}$

Q. From the sets given below, select equal set:
$A=\{2,4,8,12\},$

Q. Write down all the subsets of the following sets
(i) {a}