NCERT Solutions for Class 11-science Maths Chapter 1 - Sets

Chapter 1 - Sets Ex. 1.1

Solution 1

 Hence: this collection is a set.

 
(vii) The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection.
 
 Hence: this collection is a set.


(viii) The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter.

 Hence: this collection is a set.


(ix) The collection ofmost dangerous animals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from person to person.

 Hence: this collection is not a set.

Solution 2
Solution 3

(i) A = { x : x is an integer and -3 ≤ x < 7}.

The elements of this set are -3, -2, -1, 0, 1, 2, 3, 4, 5 and 6 only.

Therefore, the given set can written in roster form as

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

 

(ii) B = { x : x is a natural number less than 6}

The elements of this set are 1, 2, 3, 4 and 5 only.

Therefore, the given set can written in roster form as

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

 

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

The elements of this set are 17, 26, 35, 44, 53, 62, 71 and 80 only.

Therefore, the given set can written in roster form as

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

 

(iv) D = { x : x is a prime number which is divisor of 60}.

2 60
2 30
3 15
  5

∴ 60 = 2 × 2 × 3 × 5

The elements of this set are 2, 3 and 5 only.

Therefore, this set can written in roster form as D = {2, 3, 5}.

 

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

There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated.

Therefore, this set can written in roster form as

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

 

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

There are 6 letters in the word BETTER, out of which letters E and T are repeated.

Therefore, this set can written in roster form as

F = {B, E, T, R}

Solution 4
Solution 5

Solution 6

Chapter 1 - Sets Ex. 1.2

Solution 1
Solution 2
Solution 3
Solution 4
Solution 5

Chapter 1 - Sets Ex. 1.3

Solution 1

Solution 2
Solution 3

left parenthesis x i right parenthesis space T h e space s t a t e m e n t space open curly brackets empty set close curly brackets subset of A space i s space i n c o r r e c t
empty set space i s space a space s u b s e t space o f space A space a n d space i t space i s space n o t space a n space e l e m e n t space o f space A.
open curly brackets empty set close curly brackets subset of A space m e a n s space t h a t space e l e m e n t s space o f space t h e space s e t space open curly brackets empty set close curly brackets space a r e space t h e space e l e m e n t s space o f space A.
B u t space sin c e space empty set element of A space i s space i n c o r r e c t comma space open curly brackets empty set close curly brackets ⊄ A.

Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9

Chapter 1 - Sets Ex. 1.4

Solution 1

Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7

Solution 8
Solution 9
Solution 10
Solution 11
Solution 12

Chapter 1 - Sets Ex. 1.5

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5
Solution 6

Solution 7

Chapter 1 - Sets Ex. 1.6

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Chapter 1 - Sets Misc. Ex.

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16