Anand Classes provides expertly crafted Sets NCERT Solutions Class 11 Maths Exercise 1.4 Chapter 1 to help students master important concepts related to sets and their operations. These solutions are fully aligned with the latest NCERT and CBSE syllabus, offering clear, step-by-step explanations for every question. Ideal for Class 11 students preparing for exams, these solutions make understanding and applying set theory concepts simple and effective. Click the print button to download study material and notes.
NCERT Question 1. Find the union of each of the following pairs of sets:
(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = {a, e, i, o, u} B = {a, b, c}
(iii) A = {x: x is a natural number and multiple of 3}, B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and 1 < x โค 6}, B = {x: x is a natural number and 6 < x < 10},
(v) A = {1, 2, 3}, B = ฮฆ
Solution:
(i) X = {1, 3, 5} Y = {1, 2, 3}
So, the union of the pairs of set can be written as
X โช Y= {1, 2, 3, 5}
(ii) A = {a, e, i, o, u} B = {a, b, c}
So, the union of the pairs of set can be written as
Aโช B = {a, b, c, e, i, o, u}
(iii) A = {x: x is a natural number and multiple of 3} = {3, 6, 9 โฆ}
B = {x: x is a natural number less than 6} = {1, 2, 3, 4, 5, 6}
So, the union of the pairs of set can be written as
A โช B = {1, 2, 4, 5, 3, 6, 9, 12 โฆ}
Hence, A โช B = {x: x = 1, 2, 4, 5 or a multiple of 3}
(iv) A = {x: x is a natural number and 1 < x โค 6} = {2, 3, 4, 5, 6}
B = {x: x is a natural number and 6 < x < 10} = {7, 8, 9}
So, the union of the pairs of set can be written as
Aโช B = {2, 3, 4, 5, 6, 7, 8, 9}
Hence, Aโช B = {x: x โ N and 1 < x < 10}
(v) A = {1, 2, 3}, B = ฮฆ
So, the union of the pairs of set can be written as
Aโช B = {1, 2, 3}
NCERT Question 2. Let A = {a, b}, B = {a, b, c}. Is A โ B? What is A โช B?
Solution:
It is given that
A = {a, b} and B = {a, b, c}
Yes, A โ B
So, the union of the pairs of set can be written as
Aโช B = {a, b, c} = B
NCERT Question 3. If A and B are two sets such that A โ B,
then what is A โช B?
Solution:
If A and B are two sets such that A โ B, then A โช B = B.
NCERT Question 4. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8}
and D = {7, 8, 9, 10}; find
(i) A โช B (ii) A โช C (iii) B โช C (iv) B โช D (v) A โช B โช C
(vi) A โช B โช D (vii) B โช C โช D
Solution:
It is given that
A = {1, 2, 3, 4], B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}
(i) A โช B = {1, 2, 3, 4, 5, 6}
(ii) A โช C = {1, 2, 3, 4, 5, 6, 7, 8}
(iii) B โช C = {3, 4, 5, 6, 7, 8}
(iv) B โช D = {3, 4, 5, 6, 7, 8, 9, 10}
(v) A โช B โช C = {1, 2, 3, 4, 5, 6, 7, 8}
(vi) A โช B โช D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(vii) B โช C โช D = {3, 4, 5, 6, 7, 8, 9, 10}
NCERT Question 5. Find the intersection of each pair of sets:
(i) X = {1, 3, 5}, Y = {1, 2, 3}
(ii) A = {a, e, i, o, u}, B = {a, b, c}
(iii) A = {x: x is a natural number and multiple of 3}, B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and 1 < x โค 6}, B = {x: x is a natural number and 6 < x < 10}
(v) A = {1, 2, 3}, B = ฮฆ
Solution:
(i) X = {1, 3, 5}, Y = {1, 2, 3}
So, the intersection of the given set can be written as
X โฉ Y = {1, 3}
(ii) A = {a, e, i, o, u}, B = {a, b, c}
So, the intersection of the given set can be written as
A โฉ B = {a}
(iii) A = {x: x is a natural number and multiple of 3} = (3, 6, 9 โฆ}
B = {x: x is a natural number less than 6} = {1, 2, 3, 4, 5}
So, the intersection of the given set can be written as
A โฉ B = {3}
(iv) A = {x: x is a natural number and 1 < x โค 6} = {2, 3, 4, 5, 6}
B = {x: x is a natural number and 6 < x < 10} = {7, 8, 9}
So, the intersection of the given set can be written as
A โฉ B = ฮฆ
(v) A = {1, 2, 3}, B = ฮฆ
So, the intersection of the given set can be written as
A โฉ B = ฮฆ
NCERT Question 6. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find
(i) A โฉ B (ii) B โฉ C (iii) A โฉ C โฉ D (iv) A โฉ C (v) B โฉ D
(vi) A โฉ (B โช C) (vii) A โฉ D (viii) A โฉ (B โช D)
(ix) (A โฉ B) โฉ (B โช C) (x) (A โช D) โฉ (B โช C)
Solution:
(i) A โฉ B = {7, 9, 11}
(ii) B โฉ C = {11, 13}
(iii) A โฉ C โฉ D = {A โฉ C} โฉ D
= {11} โฉ {15, 17}
= ฮฆ
(iv) A โฉ C = {11}
(v) B โฉ D = ฮฆ
(vi) A โฉ (B โช C) = (A โฉ B) โช (A โฉ C)
= {7, 9, 11} โช {11}
= {7, 9, 11}
(vii) A โฉ D = ฮฆ
(viii) A โฉ (B โช D) = (A โฉ B) โช (A โฉ D)
= {7, 9, 11} โช ฮฆ
= {7, 9, 11}
(ix) (A โฉ B) โฉ (B โช C) = {7, 9, 11} โฉ {7, 9, 11, 13, 15}
= {7, 9, 11}
(x) (A โช D) โฉ (B โช C) = {3, 5, 7, 9, 11, 15, 17) โฉ {7, 9, 11, 13, 15}
= {7, 9, 11, 15}
NCERT Question 7. If A = {x: x is a natural number}, B = {x: x is an even natural number}, C = {x: x is an odd natural number} and D = {x: x is a prime number}, find
(i) A โฉ B (ii) A โฉ C (iii) A โฉ D (iv) B โฉ C (v) B โฉ D (vi) C โฉ D
Solution:
It can be written as
A = {x: x is a natural number} = {1, 2, 3, 4, 5 โฆ}
B ={x: x is an even natural number} = {2, 4, 6, 8 โฆ}
C = {x: x is an odd natural number} = {1, 3, 5, 7, 9 โฆ}
D = {x: x is a prime number} = {2, 3, 5, 7 โฆ}
(i) A โฉB = {x: x is a even natural number} = B
(ii) A โฉ C = {x: x is an odd natural number} = C
(iii) A โฉ D = {x: x is a prime number} = D
(iv) B โฉ C = ฮฆ
(v) B โฉ D = {2}
(vi) C โฉ D = {x: x is odd prime number}
NCERT Question 8. Which of the following pairs of sets are disjoint
(i) {1, 2, 3, 4} and {x: x is a natural number and 4 โค x โค 6}
(ii) {a, e, i, o, u} and {c, d, e, f}
(iii) {x: x is an even integer} and {x: x is an odd integer}
Solution:
(i) {1, 2, 3, 4}
{x: x is a natural number and 4 โค x โค 6} = {4, 5, 6}
So, we get
{1, 2, 3, 4} โฉ {4, 5, 6} = {4}
Hence, this pair of sets is not disjoint.
(ii) {a, e, i, o, u} โฉ (c, d, e, f} = {e}
Hence, {a, e, i, o, u} and (c, d, e, f} are not disjoint.
(iii) {x: x is an even integer} โฉ {x: x is an odd integer} = ฮฆ
Hence, this pair of sets is disjoint.
NCERT Question 9. If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(i) A โ B (ii) A โ C (iii) A โ D (iv) B โ A (v) C โ A
(vi) D โ A (vii) B โ C (viii) B โ D (ix) C โ B
(x) D โ B (xi) C โ D (xii) D โ C
Solution:
(i) A โ B = {3, 6, 9, 15, 18, 21}
(ii) A โ C = {3, 9, 15, 18, 21}
(iii) A โ D = {3, 6, 9, 12, 18, 21}
(iv) B โ A = {4, 8, 16, 20}
(v) C โ A = {2, 4, 8, 10, 14, 16}
(vi) D โ A = {5, 10, 20}
(vii) B โ C = {20}
(viii) B โ D = {4, 8, 12, 16}
(ix) C โ B = {2, 6, 10, 14}
(x) D โ B = {5, 10, 15}
(xi) C โ D = {2, 4, 6, 8, 12, 14, 16}
(xii) D โ C = {5, 15, 20}
NCERT Question 10. If X = {a, b, c, d} and Y = {f, b, d, g}, find
(i) X โ Y (ii) Y โ X (iii) X โฉ Y
Solution:
(i) X โ Y = {a, c}
(ii) Y โ X = {f, g}
(iii) X โฉ Y = {b, d}
NCERT Question 11. If R is the set of real numbers and Q is the set of rational numbers, then what is R โ Q?
Solution:
We know that
R โ Set of real numbers
Q โ Set of rational numbers
Hence, R โ Q is a set of irrational numbers.
NCERT Question 12. State whether each of the following statement is true or false. Justify your answer.
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.
(ii) {a, e, i, o, u } and {a, b, c, d} are disjoint sets.
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
Solution:
(i) False
If 3 โ {2, 3, 4, 5}, 3 โ {3, 6}
So, we get {2, 3, 4, 5} โฉ {3, 6} = {3}
(ii) False
If a โ {a, e, i, o, u}, a โ {a, b, c, d}
So, we get {a, e, i, o, u} โฉ {a, b, c, d} = {a}
(iii) True
Here {2, 6, 10, 14} โฉ {3, 7, 11, 15} = ฮฆ
(iv) True
Here {2, 6, 10} โฉ {3, 7, 11} = ฮฆ
