Exercise 1.1
Type 1
Question 1
Which of the following collections are sets ? Justify your answer.
(i) The collection of good cricket players of India.
(ii) The collection of most dangerous animals of the world.
(iii) The collection of all girls in your class.
(iv) The collection of novels written by writer Premchand.
(v) The collection of all even integers.
(vi) The collection of all lines in a particular plane.
(vii) The collection of beautiful girls of the world.
(viii) The collection of renowned mathematicians of the world.
Type 2
Question 2
Write the following sets in set-builder form :
(i) $A=\{-1,0,1,2,3, \ldots, 8\}$
(ii) $B=\{3,6,9,12, \ldots \ldots\}$
(iii) $C=\{1,-1, i,-i\}$
Question 3
Write the following sets in set-builder form :
(i) $A=\left\{\frac{1}{3}, \frac{2}{4}, \frac{3}{5}, \frac{4}{6}, \frac{5}{7}, \frac{6}{8}, \frac{7}{9}, \frac{8}{10}\right\}$
(ii) $B=\{1,4,9,16, \ldots\}$
(iii) $C=\{2,5,10, \ldots\}$
(iv) $D=\{5,7,11,13,17,19,23,29\}$
(v) $E=\{5,9,13,17,21, \ldots\}$
(vi) $F=\{14,21,28,35,42, \ldots, 98\}$
(vii) $G=\{1,5,10,15, \ldots\}$
Type 3
Question 4
Write the following sets in tabular form (roster form) :
$A=\{x: x$ is an integer and $-1 \leq x<9\}$
$B=\{x: x$ is an odd integer and $x>-2\}$
$C=\{x: x$ is a natural number and $5<x \leq 26\}$
$D=\{x: x=$ cube roots of unity $\}$.
$E=\left\{x: x^{2}+x-4=0\right\}$
$F=\{x: x$ is a prime number less than 24$\}$
$G=\{x: x$ is two digit number sum of whose digits is 4$\}$
$H=\left\{x: x\right.$ is a positive integer and $\left.x^{2}<40\right\}$
Question 5
Describe the following sets in roster form (tabular form) :
$A=\{x: x \in Z$ and $|x|<5\}$
$B=\{x: x$ is a letter of the word 'proportion' $\}$
$C=\left\{x: x^{3}=-1, x \in R\right\}$.
$D=\{x: x=2 n-1<20$ and $n \in N\}$
$E=\left\{x ; x=\frac{n}{n+1}, n \in N\right\}$
$F=\{x: x$ is a month of a year not having 31 days $\}$
Question 6
Write the following sets in roster form :
(i) $A=\left\{3^{n}-2^{n}: n \in N\right.$ and $\left.1 \leq n \leq 5\right\}$
(ii) $B=\left\{a_{n}: n \in N, a_{n+1}=2 a_{n}\right.$ and $\left.a_{1}=3\right\}$
(iii) $C=\left\{a_{n}: n \in N, a_{n+2}=a_{n+1}+a_{n}, a_{1}=1, a_{2}=2\right\}$
Question 7
Match each of the sets on the left described in the roster form with the same set on the right described in the set-builder form :
(i) $\{\mathrm{H}, \mathrm{A}, \mathrm{R}, \mathrm{Y}, \mathrm{N}\}$
(a) $\{x: x$ is a natural number and a divisor of 18$\}$
(ii) $\{\mathrm{L}, \mathrm{I}, \mathrm{T}, \mathrm{E}\}$
(b) $\{x: x$ is a letter of the word HARYANA $\}$
(iii) $\{1,2,3,4,6,12\}$ (c) $\{x: x$ is a letter of the word LITTLE $\}$
(iv) $\{1,2,3,6,9,18\}$
(d) $\{x: x$ is a natural number and is a divisor of 12$\}$
Type 4
Question 8
Determine the empty sets, singleton sets and pair sets in the following sets : $A=\left\{x: x^{2}=16\right.$ and $\left.2 x=5\right\}$
$B=\left\{x: x^{2}=2, x\right.$ is a rational number $\}$
$C=\{x: 3 \leq x \leq 5$ and $5 \leq x<6$, where $x$ is an integer $\}$
$D=\left\{x: x>0\right.$ and $\left.x^{2}=25\right\}$
$E=\left\{x: x^{3}+1=0\right.$ and $x$ is an integer $\}$
Question 9
Which of the following sets are empty ?
(i) The set of even prime numbers.
(ii) Set of point of intersection of two parallel lines.
(iii) Set of odd natural numbers divisible by 2 .
Question 10
Which of the following sets are empty , singleton set and pair, which of them are equal ?
$A=\left\{x: 2 x=10, x^{2}-7 x+10=0\right\}$
$B=\left\{x: x^{2}-16 x+55=0\right.$ and $\left.x^{2}=25\right\}$
$C=\left\{x:-\frac{1}{2} \leq x \leq \frac{1}{2}\right\}$
$D=\left\{x: 0 \leq 4 x^{2} \leq 1\right\}$
Question 11
Are the following sets equal ?
(i)
$\begin{aligned}&A=\{2,1\}, B=\{1,2\} \\&C=\left\{x: x^{2}-3 x+2=0\right\}\end{aligned}$
(ii) $A=\left\{x: x^{3}-8=0\right.$ and $x$ is a real number $\}$
$B=\left\{x: x^{2}+7 x-18=0 \text { and } x>0\right\}$
(iii) $A=$ The set of letters in the word 'ALLOY'.
$B=$ The set of letters in the word 'LOYAL'.
(iv) $A=\left\{x: x \in Z\right.$ and $\left.x^{2} \leq 4\right\}$.
$B=\left\{x: x \in R\right.$ and $\left.x^{2}-3 x+2=0\right\}$
(v) $A=\{x: x$ is a multiple of 10$\}$.
$B=\{10,15,20,25,30, \ldots\}$.
Question 12
Which of the following sets are infinite sets ?
(i) The set of all lines parallel to $x$-axis.
(ii) The set of all circles passing through the origin.
(iii) The set of positive integers greater than 100 .
(iv) The set of natural numbers which are multiples of $5 .$
(v) The set of prime numbers less than 99 .
(vi) The set of straight lines passing through a fixed point.
(vii) The set of all natural numbers which divide 42 .
(viii) $\{x: x \in Z$ and $x>6\}$
(ix) $\{x: x$ is people of India speaking Hindi $\}$
Question 13
From the sets given below, select the equivalent sets :
$A=\{1,2,3,5\}, B=\{5,10\}, C=\left\{x: x^{2}-5 x+4=0\right\}$
$D=\{x: x$ is a letter of the word LOVE $\}$.
$E=\{x ; x$ is a letter of the word WOLF $\}$.
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