CBSE NCERT Solutions For Class 11th Maths Chapter 1 : Set. NCERT Solutins For Class 11 Mathematics. Exercise 1.1, Exercise 1.2, Exercise 1.3, Exercise 1.4, Exercise 1.5, Exercise 1.6, (Miscellaneous Excercise) many more solutions
Exercise 1.4
Question 1:
Find the union of each of the following pairs of sets:
 X = {1, 3, 5} Y = {1, 2, 3}
 A = {a, e, i, o, u} B = {a, b, c}
 A = {x: x is a natural number and multiple of 3} B = {x: x is a natural number less than 6}
 A = {x: x is a natural number and 1 < x ≤ 6}
B = {x: x is a natural number and 6 < x < 10}
(v) A = {1, 2, 3}, B = Φ
Answer
 X = {1, 3, 5} Y = {1, 2, 3} X∪ Y= {1, 2, 3, 5}
 A = {a, e, i, o, u} B = {a, b, c}
A∪ B = {a, b, c, e, i, o, u}
(iii) A = {x: x is a natural number and multiple of 3} = {3, 6, 9 …} As B = {x: x is a natural number less than 6} = {1, 2, 3, 4, 5, 6} A ∪ B = {1, 2, 4, 5, 3, 6, 9, 12 …}
∴ A ∪ B = {x: x = 1, 2, 4, 5 or a multiple of 3}
(iv) A = {x: x is a natural number and 1 < x ≤ 6} = {2, 3, 4, 5, 6} B = {x: x is a natural number and 6 < x < 10} = {7, 8, 9}
A∪ B = {2, 3, 4, 5, 6, 7, 8, 9}
∴ A∪ B = {x: x ∈ N and 1 < x < 10}
(v) A = {1, 2, 3}, B = Φ A∪ B = {1, 2, 3}
Question 2:
Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?
Answer
Here, A = {a, b} and B = {a, b, c}
Yes, A ⊂ B.
A∪ B = {a, b, c} = B
Question 3:
If A and B are two sets such that A ⊂ B, then what is A ∪ B?
Answer
If A and B are two sets such that A ⊂ B, then A ∪ B = B.
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
 A ∪ B
 A ∪ C
 B ∪ C
 B ∪ D
 A ∪ B ∪ C
 A ∪ B ∪ D
(vii) B ∪ C ∪ D
Answer
A = {1, 2, 3, 4], B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}
 A ∪ B = {1, 2, 3, 4, 5, 6}
 A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
 B ∪ C = {3, 4, 5, 6, 7, 8}
 B ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}
 A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
 A ∪ B ∪ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(vii) B ∪ C ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}
Question 5:
Find the intersection of each pair of sets:
 X = {1, 3, 5} Y = {1, 2, 3}
 A = {a, e, i, o, u} B = {a, b, c}
 A = {x: x is a natural number and multiple of 3} B = {x: x is a natural number less than 6}
 A = {x: x is a natural number and 1 < x ≤ 6}
B = {x: x is a natural number and 6 < x < 10}
(v) A = {1, 2, 3}, B = Φ
Answer

 X = {1, 3, 5}, Y = {1, 2, 3} X ∩ Y = {1, 3}
 A = {a, e, i, o, u}, B = {a, b, c} A ∩ B = {a}
 A = {x: x is a natural number and multiple of 3} = (3, 6, 9 …} B = {x: x is a natural number less than 6} = {1, 2, 3, 4, 5}
 A ∩ B = {3}

 A = {x: x is a natural number and 1 < x ≤ 6} = {2, 3, 4, 5, 6} B = {x: x is a natural number and 6 < x < 10} = {7, 8, 9}

A ∩ B = Φ


 A = {1, 2, 3}, B = Φ

A ∩ B = Φ
Question 6:
If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find
 A ∩ B
 B ∩ C
 A ∩ C ∩ D
 A ∩ C
 B ∩ D
 A ∩ (B ∪ C)
 A ∩ D
 A ∩ (B ∪ D)
 (A ∩ B) ∩ (B ∪ C)
 (A ∪ D) ∩ (B ∪ C) Answer
 A ∩ B = {7, 9, 11}
 B ∩ C = {11, 13}
 A ∩ C ∩ D = { A ∩ C} ∩ D = {11} ∩ {15, 17} = Φ
 A ∩ C = {11}
 B ∩ D = Φ
 A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
 {7, 9, 11} ∪ {11} = {7, 9, 11}

 A ∩ D = Φ
 A ∩ (B ∪ D) = (A ∩ B) ∪ (A ∩ D)

 {7, 9, 11} ∪ Φ = {7, 9, 11}

 (A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}
 (A ∪ D) ∩ (B ∪ C) = {3, 5, 7, 9, 11, 15, 17) ∩ {7, 9, 11, 13, 15}

 {7, 9, 11, 15}
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
 A ∩ B
 A ∩ C
 A ∩ D
 B ∩ C
 B ∩ D
 C ∩ D Answer
A = {x: x is a natural number} = {1, 2, 3, 4, 5 …}
B ={x: x is an even natural number} = {2, 4, 6, 8 …} C = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}
D = {x: x is a prime number} = {2, 3, 5, 7 …}
 A ∩B = {x: x is a even natural number} = B
 A ∩ C = {x: x is an odd natural number} = C
 A ∩ D = {x: x is a prime number} = D
 B ∩ C = Φ
 B ∩ D = {2}
 C ∩ D = {x: x is odd prime number}
Question 8:
Which of the following pairs of sets are disjoint
 {1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6}
 {a, e, i, o, u}and {c, d, e, f}
 {x: x is an even integer} and {x: x is an odd integer} Answer
 {1, 2, 3, 4}
{x: x is a natural number and 4 ≤ x ≤ 6} = {4, 5, 6} Now, {1, 2, 3, 4} ∩ {4, 5, 6} = {4}
Therefore, this pair of sets is not disjoint.
(ii) {a, e, i, o, u} ∩ (c, d, e, f} = {e}
Therefore, {a, e, i, o, u} and (c, d, e, f} are not disjoint.
(iii) {x: x is an even integer} ∩ {x: x is an odd integer} = Φ Therefore, this pair of sets is disjoint.
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
 A – B
 A – C
 A – D
 B – A
 C – A
 D – A
 B – C
 B – D
 C – B
 D – B
 C – D
 D – C Answer
 A – B = {3, 6, 9, 15, 18, 21}
 A – C = {3, 9, 15, 18, 21}
 A – D = {3, 6, 9, 12, 18, 21}
 B – A = {4, 8, 16, 20}
 C – A = {2, 4, 8, 10, 14, 16}
 D – A = {5, 10, 20}
 B – C = {20}
 B – D = {4, 8, 12, 16}
 C – B = {2, 6, 10, 14}
 D – B = {5, 10, 15}
 C – D = {2, 4, 6, 8, 12, 14, 16}
 D – C = {5, 15, 20}
Question 10:
If X = {a, b, c, d} and Y = {f, b, d, g}, find
 X – Y
 Y – X
 X ∩ Y Answer
 X – Y = {a, c}
 Y – X = {f, g}
(iii) X ∩ Y = {b, d}
Question 11:
If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q? Answer
R: set of real numbers Q: set of rational numbers
Therefore, R – Q is a set of irrational numbers.
Question 12:
State whether each of the following statement is true or false. Justify your answer.
 {2, 3, 4, 5} and {3, 6} are disjoint sets.
 {a, e, i, o, u } and {a, b, c, d} are disjoint sets.
 {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
 {2, 6, 10} and {3, 7, 11} are disjoint sets. Answer
 False
As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6}
⇒ {2, 3, 4, 5} ∩ {3, 6} = {3}
(ii) False
As a ∈ {a, e, i, o, u}, a ∈ {a, b, c, d}
⇒ {a, e, i, o, u } ∩ {a, b, c, d} = {a}
(iii) True
As {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ
(iv) True
As {2, 6, 10} ∩ {3, 7, 11} = Φ
NCERT Solutions for Class XI Maths: Chapter 1 – Set

Exercise 1.1 Solutions

Exercise 1.2 Solutions

Exercise 1.3 Solutions

Exercise 1.4 Solutions

Exercise 1.5 Solutions

Exercise 1.6 Solutions

Miscellaneous Solutions