SETS NCERT Solutions Exercise 1.4 for Class 11 Maths focus on set operations such as union, intersection, difference, and complement. This exercise helps students apply concepts of sets in solving problems using formulas and Venn diagrams. It is an important part of Class 11 CBSE Mathematics and is highly useful for competitive exams of India.
Chapter 1 SETS Exercise 1.4 NCERT Solutions for Class 11 Maths
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 β€ 6}, B = {x: x is a natural number and 6 < x < 10},
(v) A = {1, 2, 3}, B = Ξ¦
Solution:
(i) X = {1, 3, 5} Y = {1, 2, 3}
So, the union of the pairs of set can be written as
X βͺ 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
Aβͺ B = {a, b, c, e, i, o, u}
(iii) A = {x: x is a natural number and multiple of 3} = {3, 6, 9 β¦}
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 βͺ B = {1, 2, 4, 5, 3, 6, 9, 12 β¦}
Hence, A βͺ B = {x: x = 1, 2, 4, 5 or a multiple of 3}
(iv) A = {x: x is a natural number and 1 < x β€ 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
Aβͺ B = {2, 3, 4, 5, 6, 7, 8, 9}
Hence, Aβͺ B = {x: x β N and 1 < x < 10}
(v) A = {1, 2, 3}, B = Ξ¦
So, the union of the pairs of set can be written as
Aβͺ B = {1, 2, 3}
NCERT Question 2. Let A = {a, b}, B = {a, b, c}. Is A β B? What is A βͺ B?
Solution:
It is given that
A = {a, b} and B = {a, b, c}
Yes, A β B
So, the union of the pairs of set can be written as
Aβͺ B = {a, b, c} = B
NCERT Question 3. If A and B are two sets such that A β B,
then what is A βͺ B?
Solution:
If A and B are two sets such that A β B, then A βͺ 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 βͺ B (ii) A βͺ C (iii) B βͺ C (iv) B βͺ D (v) A βͺ B βͺ C
(vi) A βͺ B βͺ D (vii) B βͺ C βͺ 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 βͺ B = {1, 2, 3, 4, 5, 6}
(ii) A βͺ C = {1, 2, 3, 4, 5, 6, 7, 8}
(iii) B βͺ C = {3, 4, 5, 6, 7, 8}
(iv) B βͺ D = {3, 4, 5, 6, 7, 8, 9, 10}
(v) A βͺ B βͺ C = {1, 2, 3, 4, 5, 6, 7, 8}
(vi) A βͺ B βͺ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(vii) B βͺ C βͺ 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 β€ 6}, B = {x: x is a natural number and 6 < x < 10}
(v) A = {1, 2, 3}, B = Ξ¦
Solution:
(i) X = {1, 3, 5}, Y = {1, 2, 3}
So, the intersection of the given set can be written as
X β© 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 β© B = {a}
(iii) A = {x: x is a natural number and multiple of 3} = (3, 6, 9 β¦}
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 β© B = {3}
(iv) A = {x: x is a natural number and 1 < x β€ 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 β© B = Ξ¦
(v) A = {1, 2, 3}, B = Ξ¦
So, the intersection of the given set can be written as
A β© B = Ξ¦
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 β© B (ii) B β© C (iii) A β© C β© D (iv) A β© C (v) B β© D
(vi) A β© (B βͺ C) (vii) A β© D (viii) A β© (B βͺ D)
(ix) (A β© B) β© (B βͺ C) (x) (A βͺ D) β© (B βͺ C)
Solution:
(i) A β© B = {7, 9, 11}
(ii) B β© C = {11, 13}
(iii) A β© C β© D = {A β© C} β© D
= {11} β© {15, 17}
= Ξ¦
(iv) A β© C = {11}
(v) B β© D = Ξ¦
(vi) A β© (B βͺ C) = (A β© B) βͺ (A β© C)
= {7, 9, 11} βͺ {11}
= {7, 9, 11}
(vii) A β© D = Ξ¦
(viii) A β© (B βͺ D) = (A β© B) βͺ (A β© D)
= {7, 9, 11} βͺ Ξ¦
= {7, 9, 11}
(ix) (A β© B) β© (B βͺ C) = {7, 9, 11} β© {7, 9, 11, 13, 15}
= {7, 9, 11}
(x) (A βͺ D) β© (B βͺ C) = {3, 5, 7, 9, 11, 15, 17) β© {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 β© B (ii) A β© C (iii) A β© D (iv) B β© C (v) B β© D (vi) C β© D
Solution:
It can be written as
A = {x: x is a natural number} = {1, 2, 3, 4, 5 β¦}
B ={x: x is an even natural number} = {2, 4, 6, 8 β¦}
C = {x: x is an odd natural number} = {1, 3, 5, 7, 9 β¦}
D = {x: x is a prime number} = {2, 3, 5, 7 β¦}
(i) A β©B = {x: x is a even natural number} = B
(ii) A β© C = {x: x is an odd natural number} = C
(iii) A β© D = {x: x is a prime number} = D
(iv) B β© C = Ξ¦
(v) B β© D = {2}
(vi) C β© 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 β€ x β€ 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 β€ x β€ 6} = {4, 5, 6}
So, we get
{1, 2, 3, 4} β© {4, 5, 6} = {4}
Hence, this pair of sets is not disjoint.
(ii) {a, e, i, o, u} β© (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} β© {x: x is an odd integer} = Ξ¦
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 β B (ii) A β C (iii) A β D (iv) B β A (v) C β A
(vi) D β A (vii) B β C (viii) B β D (ix) C β B
(x) D β B (xi) C β D (xii) D β C
Solution:
(i) A β B = {3, 6, 9, 15, 18, 21}
(ii) A β C = {3, 9, 15, 18, 21}
(iii) A β D = {3, 6, 9, 12, 18, 21}
(iv) B β A = {4, 8, 16, 20}
(v) C β A = {2, 4, 8, 10, 14, 16}
(vi) D β A = {5, 10, 20}
(vii) B β C = {20}
(viii) B β D = {4, 8, 12, 16}
(ix) C β B = {2, 6, 10, 14}
(x) D β B = {5, 10, 15}
(xi) C β D = {2, 4, 6, 8, 12, 14, 16}
(xii) D β C = {5, 15, 20}
NCERT Question 10. If X = {a, b, c, d} and Y = {f, b, d, g}, find
(i) X β Y (ii) Y β X (iii) X β© Y
Solution:
(i) X β Y = {a, c}
(ii) Y β X = {f, g}
(iii) X β© 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 β Q?
Solution:
We know that
R β Set of real numbers
Q β Set of rational numbers
Hence, R β 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 β {2, 3, 4, 5}, 3 β {3, 6}
So, we get {2, 3, 4, 5} β© {3, 6} = {3}
(ii) False
If a β {a, e, i, o, u}, a β {a, b, c, d}
So, we get {a, e, i, o, u} β© {a, b, c, d} = {a}
(iii) True
Here {2, 6, 10, 14} β© {3, 7, 11, 15} = Ξ¦
(iv) True
Here {2, 6, 10} β© {3, 7, 11} = Ξ¦
Important Chapter Links
Sets Exercise 1.4 of Class 11 NCERT Mathematics covers important concepts of set operations including union, intersection, difference, and complement. This exercise helps students understand how to perform operations on sets and solve problems using Venn diagrams. It also introduces key properties and laws of sets that simplify calculations. With detailed solutions and examples, this exercise strengthens problem-solving skills and is highly useful for CBSE exams and competitive exams of India.
FAQs of Chapter-1 Sets Exercise 1.4 NCERT Solutions for Class 11 Maths
What is Exercise 1.4 about?
It focuses on set operations such as union, intersection, difference, and complement.
What is the union of two sets?
It includes all elements from both sets.
What is the intersection of two sets?
It includes only common elements of both sets.
What is the difference between two sets?
It includes elements that are in one set but not in the other.
What is complement of a set?
It includes elements not present in the set but in the universal set.
Why are Venn diagrams important in this exercise?
They help visualize set operations and solve problems easily.
Is Exercise 1.4 important for exams?
Yes, it is very important for CBSE and competitive exams.
Are NCERT solutions enough for preparation?
Yes, they provide a strong base and are sufficient for CBSE exams.
Important Chapter Links
Sets Exercise 1.4 of Class 11 NCERT Mathematics covers important concepts of set operations including union, intersection, difference, and complement. This exercise helps students understand how to perform operations on sets and solve problems using Venn diagrams. It also introduces key properties and laws of sets that simplify calculations. With detailed solutions and examples, this exercise strengthens problem-solving skills and is highly useful for CBSE exams and competitive exams of India.
Exercise-wise NCERT Solutions
- Basic definition of sets
- Writing sets in roster and set-builder form
- Types of sets
- Finite and infinite sets
- Subsets and proper subsets
- Number of subsets
Exercise 1.4
- Set operations (union, intersection, complement)
- Advanced problems on set operations and Venn diagrams
- Mixed problems covering all concepts of the chapter