NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3 are the part of NCERT Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3.


Ex 1.3 Class 11 Maths Question 1.

Make correct statements by filling in the symbols or in the 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 is a 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}

Solution.
(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 a 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}

 

Ex 1.3 Class 11 Maths Question 2.

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

Solution.


Ex 1.3 Class 11 Maths Question 3.

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4} 
 A
(ii) {3, 4} 
 A
(iii) {{3, 4}} 
 A
(iv) 1 
 A
(v) 1 
 A
(vi) {1, 2, 5} 
 A
(vii) {1, 2, 5} 
 A
(viii) {1, 2, 3} 
 A
(ix) Ø 
 A
(x) Ø 
 A
(xi) {Ø} 
 A


Solution.


Ex 1.3 Class 11 Maths Question 4.

Write down all the subsets of the following sets:
(i)
 {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) φ

Solution.
(i) {a}

Number of elements in the given set = 1
Number of subsets of the given set = 21 = 2
Subsets of the given set are φ, {a}.

(ii) {a, b}

Number of elements in the given set = 2
Number of subsets of the given set = 22 = 4
Subsets of the given set are φ, {a}, {b}, {a, b}.

(iii) {1, 2, 3}

Number of elements in the given set = 3
Number of subsets of the given set = 23 = 8
Subsets of the given set are φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}.

(iv) φ

Number of elements in the given set = 0
Number of subsets of the given set = 20= 1
Subset of the given set is φ.


Ex 1.3 Class 11 Maths Question 5.

How many elements has P(A), if A = φ?

Solution.
Number of elements in set A = 0
Number of subsets of set A = 20 = 1
Hence, the number of elements of P(A) is 1.

Ex 1.3 Class 11 Maths Question 6.

Write the following as intervals:
(i)
 {x: x
R, -4 < x ≤ 6}
(ii) {x: x
R, -12 < x < -10}
(iii) {x: x
R, 0 ≤ x < 7}
(iv) {x: x
R, 3 ≤ x ≤ 4}

Solution.
(i) Let A = {x: x
R, -4 < x ≤ 6}
It can be written in the form of interval as (-4, 6]
(ii) Let A = {x: x
R, -12 < x < -10}
It can be written in the form of interval as (-12, -10)
(iii) Let A = {x: x
R, 0 ≤ x < 7}
It can be written in the form of interval as [0, 7).
(iv) Let A = {x: x
R, 3 ≤ x ≤ 4}
It can be written in the form of interval as [3, 4].

Ex 1.3 Class 11 Maths Question 7.

Write the following intervals in set-builder form:
(i)
 (-3, 0)
(ii) [6, 12]
(iii) (6, 12]
(iv) [-23, 5)

Solution.
(i) The interval (-3, 0) can be written in set-builder form as {x: x
R, -3 < x < 0}.
(ii) The interval [6, 12] can be written in set-builder form as {x: x
R, 6 ≤ x ≤ 12}.
(iii) The interval (6, 12] can be written in set-builder form as {x: x
R, 6 < x ≤ 12}
(iv) The interval [-23, 5) can be written in set-builder form as {x: x
R, -23 ≤ x < 5}

Ex 1.3 Class 11 Maths Question 8.

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

Solution.
(i) Right triangle is a type of triangle. So, the set of triangles contain all types of triangles.
U = {x: x is a triangle in a plane}

(ii) Isosceles triangle is a type of triangle. So, the set of triangles contain all types of triangles.
U = {x: x is a triangle in a plane}

Ex 1.3 Class 11 Maths Question 9.

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set(s) for all the three sets A, B and C?
(i) {0, 1, 2, 3, 4, 5, 6}
(ii) φ
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}

Solution.
(i) {0, 1, 2, 3, 4, 5, 6} is not a universal set for A, B, C because 8
C but 8 is not a member of {0, 1, 2, 3, 4, 5, 6}.
(ii) φ is a set which contains no element. So, it is not a universal set for A, B, C.
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for A, B, C because all members of A, B, C are present in {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(iv) {1, 2, 3, 4, 5, 6, 7, 8} is not a universal set for A, B, C because 0
C but 0 is not a member of {1, 2, 3, 4, 5, 6, 7, 8}.


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