NCERT Solutions for Exercise 1.1 Class 11 Maths Chapter 1 - Sets

Question:1(i) Which of the following are sets ?justify your answer

The collection of all the months of a year beginning with the letter J.

Answer:

The months starting with letter J are:

january

june

july

Hence,this is collection of well defined objects so it is a set.

Question:1(ii) Which of the following are sets ?justify your answer

The collection of ten most talented writers of India.

Answer:

Ten most talented writers may be different depending on different criteria of determining talented writers.

Hence, this is not well defined so cannot be a set.

Question:1(iii) Which of the following are sets ?justify your answer

A team of eleven best-cricket batsmen of the world.

Answer:

Eleven most talented cricketers may be different depending on criteria of determining talent of a player.

Hence,this is not well defined so it is not a set.

Question:1(iv) Which of the following are sets ?justify your answer

The collection of all the boys in your class.

Answer:

The collection of boys in a class are well defined and known.

Group of well defined objects is a set.

Hence, it is a set.

Question:1(v) Which of the following are sets? Justify your answer

The collection of all natural numbers less than 100.

Answer:

Natural numbers less than 100 has well defined and known collection of numbers.

that is S= {1,2,3............99}

Hence,it is a set.

Question:1(vi) Which of the following are sets? Justify your answer

A collection of novels written by the writer Munshi Prem Chand.

Answer:

The collection of novels written by Munshi Prem Chand is well defined and known .

Hence,it is a set.

Question:1(vii) Which of the following are sets? Justify your answer

The collection of all even integers.

Answer:

The collection of even intergers is well defined because we can get even integers till infinite. that is

Hence,it is a set.

Question:1(viii) Which of the following are sets? Justify your answer

The collection of questions in this Chapter.

Answer:

Collection of questions in a chapter is well defined and known.

Hence ,it is a set.

Question:1(ix) Which of the following are sets? Justify your answer

A collection of the most dangerous animals of the world.

Answer:

A Collection of the most dangerous animal is not well defined because the criteria of defining the dangerousness of any animal can vary .

Hence,it is not a set.

Question:2 $LetA=\{1,2,3,4,5,6\}.Inserttheappropriatesymbol\in or\notin intheblankspace:$

(i) 5_____A

(ii) 8_____A

(iii) 0_____A

(iv) 4_____A

(v) 2_____A

(vi) 10____A

Answer:

A = $\{1,2,3,4,5,6\}$ ,the elements which lie in this set belongs to this set and others do not belong.

(i) 5 $\in$ A

(ii) 8 $\notin$ A

(iii) 0 $\notin$ A

(iv) 4 $\in$ A

(v) 2 $\in$ A

(vi) 10 $\notin$ A

Question:3(i) Write the following sets in roster form

$(i)A=\{x:xisanintegerand-3\le x<7\}$

Answer:

Elements of this set are:-3,-2,-1,0,1,2,3,4,5,6.

Hence ,this can be written as:

A = $\{-3,-2,-1,0,1,2,3,4,5,6\}$

Question:3(ii) Write the following sets in roster form

$\left(ii\right)B=\{x:xisanaturalnumberlessthan6\}$

Answer:

Natural numbers less than 6 are: 1,2,3,4,5.

This can be written as:

$B=\{1,2,3,4,5\}$

Question:3(iii) Write the following sets in roster form

C = {x : x is a two-digit natural number such that the sum of its digits is 8}

Answer:

The two digit numbers having sum equal to 8 are: 17,26,35,44,53,62,71,80.

This can be written as:

$C=\{17,26,35,44,53,62,71,80\}$

Question:3(iv) Write the following sets in roster form

D = {x : x is a prime number which is divisor of 60}

Answer:

$60=2\ast 2\ast 3\ast 5$

Prime numbers which are divisor of 60 are:2,3,5.

This can be written as:

$D=\{2,3,5\}$

Question:3(v) Write the following sets in roster form

E = The set of all letters in the word TRIGONOMETRY.

Answer:

Letters of word TRIGONOMETRY are:T,R,I,G,N,O,M,E,Y.

This can be written as :

E = {T,R,I,G,N,O,M,E,Y}

Question:3(vi) Write the following sets in roster form

F = The set of all letters in the word BETTER.

Answer:

The set of letters of word BETTER are: {B,E,T,R}

This can be written as:

F = {B,E,T,R}

Question:4(i) Write the following sets in the set builder form

{3, 6, 9, 12}

Answer:

A = {3,6,9,12}

This can be written as : $\{3,6,9,12\}=\{x:x=3n,n\in Nand1\le n\le 4\}$

Question:4(ii) Write the following sets in the set builder form

{2,4,8,16,32}

Answer:

$2=2^1$

$4=2^2$

$8=2^3$

$16=2^4$

$32=2^5$

$\{2,4,8,16,32\}$ can be written as $\{x:x=2^n,n\in Nand1\le n\le 5\}.$

Question:4(iii) Write the following sets in the set builder form:

{5, 25, 125, 625}

Answer:

$5=5^1$

$25=5^2$

$125=5^3$

$625=5^4$

$\{5,25,125,625\}$ can be written as $\{x:x=5^n,n\in Nand1\le n\le 4\}$

Question:4(iv) Write the following sets in the set builder form:

{2, 4, 6, . . .}

Answer:

This is a set of all even natural numbers.

{2,4,6....} can be written as {x : x is an even natural number}

Question:4(v) Write the following sets in the set builder form :

{1,4,9, . . .,100}

Answer:

$1=1^2$

$4=2^2$

$9=3^2$

.

.

.

.

$100={10}^2$

$\{1,4,9.....100\}$ can be written as $\{x:x=n^2,n\in Nand1\le n\le 10\}$

Question:5(i) List all the elements of the following sets:

A = {x : x is an odd natural number}.

Answer:

A = { x : x is an odd natural number } = {1,3,5,7,9,11,13.............}

Question:5(ii) List all the elements of the following sets:

B= { x : x is an integer, $\frac{-1}{2}<x<\frac{9}{2}$ }

Answer:

Intergers between $-\frac{1}{2}<x<\frac{9}{2}$ are 0,1,2,3,4.

Hence,B = {0,1,2,3,4}

Question:5(iii) List all the elements of the following sets:

C = {x : x is an integer, $x^2\le 4$}

Answer:

${(-2)}^2=4$

${(-1)}^2=1$

${\left(0\right)}^2=0$

${\left(1\right)}^2=1$

${\left(2\right)}^2=4$

Integers whose square is less than or equal to 4 are : -2,-1,0,1,2.

Hence,it can be written as c = {-2,-1,0,1,2}.

Question:5(iv) List all the elements of the following sets:

D = {x : x is a letter in the word “LOYAL”}

Answer:

LOYAL has letters L,O,Y,A.

D = {x : x is a letter in the word “LOYAL”} can be written as {L,O,Y,A}.

Question:5(v) List all the elements of the following sets:

E = {x : x is a month of a year not having 31 days}

Answer:

The months not having 31 days are:

February

April

June

September

November

It can be written as {february,April,June,September,november}

Question:5(vi) List all the elements of the following sets :

F = {x : x is a consonant in the English alphabet which precedes k }.

Answer:

The consonents in english which precedes K are : B,C,D,F,G,H,J

Hence, F = {B,C,D,F,G,H,J}.

Question:6 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 of 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 is a letter of the word MATHEMATICS}.

Answer:

(i) 1,2,3,6 all are natural numbers and also divisors of 6.

Hence,(i) matches with (c)

(ii) 2,3 are prime numbers and are divisors of 6.

Hence,(ii) matches with (a).

(iii) M,A,T,H,E,I,C,S are letters of word "MATHEMATICS".

Hence, (iii) matches with (d).

(iv) 1,3,5,7,9 are odd natural numbers less than 10.

Hence,(iv) matches with (b).