Exercise 1.1 (Revised) - Chapter 1 -Sets - Ncert Solutions class 11 - Maths

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Chapter 1 - Sets | NCERT Solutions for Class 11 Maths

Ex 1.1 Question 1.

Which of the following are sets? Justify your answer.
(i) The collection of all the months of a year beginning with the letter $\mathrm{J}$.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-Cricket batmen 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 the chapter.
(ix) A collection of most dangerous animals of the world.

Answer.

(i) The collection of all months of a year beginning with J is \{January, June, July\}, which is well defined and hence it forms a set.
(ii) The collection of most talented writers of India is not well defined because opinions about 'most talented writers' vary from person to person and hence it does not form a set.
(iii) A team of eleven best-cricket batmen of the world us not well defined because opinion about 'best-cricket batsmen' vary from person to person and hence it does not form a set.

(iv) The collection of all boys in your class is well defined and hence it forms a set.
(v) The collection of all natural numbers less than 100 is $\{1,2,3$, $\qquad$ $99\}$ which is well defined and hence it forms a set.

(vi) A collection of novels written by the writer Munshi Prem Chand is well defined and hence it forms a set.
(vii) The collection al all even integers is $\qquad$ $-4,-2,0,2,4$ $\qquad$ which is well defined and hence it forms a set.
(viii) The collection of questions in this chapter is well defined and hence it forms a set.
(ix) A collection of most dangerous animals of the world is not well defined because opinion about 'most dangerous animals' vary from person to person and hence it does not form a set.
Ex 1.1 Question 2.

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

Answer.

Given: $\mathrm{A}=\{1,2,3,4,5,6\}$

(i) 5 is an element of set $\mathrm{A}$
$
\therefore 5 \in \mathrm{A}
$
(ii) 8 is not an element of set A
$
\therefore 8 \notin \mathrm{A}
$
(iii) 0 is not an element of set $\mathrm{A}$
$
\therefore 0 \text { A }
$
(iv) 4 is an element of set $\mathrm{A}$

$
\therefore 4 \in \mathrm{A}
$
(v) 2 is an element of set $\mathrm{A}$
$
\therefore 2 \in \mathrm{A}
$
(vi) 10 is not an element of set $\mathrm{A}$
$
\therefore 10 \text { \& }
$
Ex 1.1 Question 3.

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

Answer.

(i) $\mathrm{A}=\{x ; x$ is an integer and $-3 (ii) $B=\{x: x$ is a natural number less than 6$\} \therefore B=\{1,2,3,45\}$

(iii) $\mathrm{C}=\{x: x$ is a two-digit natural number such that the sum of its digits is 8$\}$
$
\therefore C=\{17,26,35,44,53,62,71,80\}
$
(iv) $\mathrm{D}=\{x: x$ is a prime number which is divisor of 60$\}$
$
\therefore \mathrm{D}=\{2,3,5\}
$
(v) $\mathrm{E}=$ The set of all letters in the word TRIGONOMETRY
$
\therefore E=\{T, R, I, G, O, N, M, E, Y\}
$
(vi) $\mathrm{F}=$ The set of all letters in the word BETTER

$
\therefore F=\{B, E, T, R\}
$
Ex 1.1 Question 4.

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) $\{2,4,6, \ldots \ldots\}$
(v) $\{1,4,9$, $\qquad$ $100\}$

Answer.

(i) Let $A=\{3,6,9,12\}$.

Here all objects of the set are natural numbers that are multiples of 3 .
$
\therefore \mathrm{A}=\{x: x=3 n, n \in \mathrm{N} \text { and } 1 \leq n \leq 4\}
$
(ii) Let $B=\{2,4,8,16,32\}$

Here all objects of the set are natural numbers that are power of 2 .
$
\therefore \mathrm{B}=\left\{x: x=2^n, n \in \mathrm{N} \text { and } 1 \leq n \leq 5\right\}
$
(iii) Let $\mathrm{C}=\{5,25,125,625\}$

Here all objects of the set are natural numbers that are power of 5 .
$
\therefore C=\left\{x ; x=5^n, n \in \mathrm{N} \text { and } 1 \leq n \leq 4\right\}
$
(iv) Let $\mathrm{D}=\{2,4,6, \ldots \ldots\}$

Here all objects of the set are even natural numbers.
$
\therefore \mathrm{D}=\{x: x \text { is an even natural number }\}
$
(v) Let $E=\{1,4,9$, $\qquad$ $100\}$

Here all objects of the set are perfect square.
$
\therefore \mathrm{D}=\left\{x ; x=n^2 \text { and } 1 \leq n \leq 10\right\}
$
Ex 1.1 Question 5.

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

Answer.

(i) $\mathrm{A}=\{x: x$ is an odd natural number $\}$
$
\therefore A=\{1,3,5,7, \ldots \ldots .\}
$
(ii) $\mathrm{B}=\left\{x: x\right.$ is an integer, $\left.-\frac{1}{2}

$
\therefore B=\{0,1,2,3,4\}
$
(iii) $\mathrm{C}=\left\{x: x\right.$ is an integer, $\left.x^2 \leq 4\right\}$
$
\therefore C=\{-2,-1,0,1,2\}
$
(iv) $\mathrm{D}=\{x: x$ is a letter in the word "LOYAL" $\}$
$$
\therefore \mathrm{D}=\{\mathrm{L}, \mathrm{O}, \mathrm{Y}, \mathrm{A}\}
$
(v) $\mathrm{E}=\{x: x$ is a month of a year not having 31 days $\}$
$\therefore E=\{$ February, April, June, September, November $\}$

(vi) $\mathrm{F}=\{x: x$ is a consonant in the English alphabet which precedes $\mathrm{K}\}$
$
\therefore F=\{B, C, D, F, G, H, J\}
$
Ex 1.1 Question 6.

Match each of the set on the left in the roster form with the same set on the right described in the 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) $\{\mathrm{M}, \mathrm{A}, \mathrm{T}, \mathrm{H}, \mathrm{E}, \mathrm{I}, \mathrm{C}, \mathrm{S}\}$
(c) $\{x: x$ is a natural number and divisor of 6$\}$
(iv) $\{!, 3,5,7,9\}$
(d) $\{x: x$ is a letter of word "MATHEMATICS" $\}$

Answer.

The sets which are in set-builder form can be written as
(a) $\{x: x$ is a prime number and a divisor of 6$\}=\{2,3\}$
(b) $\{x: x$ is an odd natural number less than 10$\}=\{1,3,5,7,9\}$

(c) $\{x: x$ is a natural number and divisor of 6$\}=\{1,2,3,6\}$
(d) $\{x: x$ is a letter of word "MATHEMATICS" $\}=\{\mathrm{M}, \mathrm{A}, \mathrm{T}, \mathrm{H}, \mathrm{E}, \mathrm{I}, \mathrm{C}, \mathrm{S}\}$

Hence the correct matching is:
(i) $\rightarrow$ (c)
(ii) $\rightarrow$ (a)
(iii) $\rightarrow$ (d)
(iv) $\rightarrow$ (b)