# NCERT Solutions for Class 11 Maths Chapter 1- Sets Exercise 1.4

The fourth exercise of this chapter revolves around some of the most important topics of the Sets. The NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.4 are created by subject experts according to the latest CBSE Syllabus 2023-24. Exercise 1.4 of NCERT Solutions for Class 11 Maths Chapter 1- Sets is based on the following topics:

1. Venn Diagrams
2. Operations on Sets
1. Union of sets
2. Intersection of sets
3. Difference of sets

The NCERT Solutions are prepared with the utmost care by the subject-matter experts present here. Students can view as well as download the NCERT Solutions for Class 11 at BYJUâ€™S and kickstart their exam preparations.

## NCERT Solutions for Class 11 Maths Chapter 1 â€“ Sets Exercise 1.4

### Class 11 Maths Chapter 1- Sets Exercise 1.4 Solutioins

1. Find the union of each of the following pairs of sets:

(i)Â X = {1, 3, 5} Y = {1, 2, 3}

(ii)Â A = {a,Â e,Â i,Â o,Â u} B = {a,Â b,Â c}

(iii)Â A = {x:Â xÂ is a natural number and multiple of 3}

B = {x:Â xÂ is a natural number less than 6}

(iv)Â A = {x:Â xÂ is a natural number and 1 <Â xÂ â‰¤Â 6}

B = {x:Â xÂ is a natural number and 6 <Â xÂ < 10}

(v)Â A = {1, 2, 3}, B =Â Î¦

Solution:

(i)Â X = {1, 3, 5} Y = {1, 2, 3}

So the union of the pairs of set can be written as

X âˆªÂ Y= {1, 2, 3, 5}

(ii)Â A = {a,Â e,Â i,Â o,Â u} B = {a,Â b,Â c}

So the union of the pairs of set can be written as

AâˆªÂ B = {a,Â b,Â c,Â e,Â i,Â o,Â u}

(iii)Â A = {x:Â xÂ is a natural number and multiple of 3} = {3, 6, 9 â€¦}

B = {x:Â xÂ 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

AÂ âˆªÂ B = {1, 2, 4, 5, 3, 6, 9, 12 â€¦}

Hence, AÂ âˆªÂ B = {x:Â xÂ = 1, 2, 4, 5 or a multiple of 3}

(iv)Â A = {x:Â xÂ is a natural number and 1 <Â xÂ â‰¤Â 6} = {2, 3, 4, 5, 6}

B = {x:Â xÂ is a natural number and 6 <Â xÂ < 10} = {7, 8, 9}

So the union of the pairs of set can be written as

AâˆªÂ B = {2, 3, 4, 5, 6, 7, 8, 9}

Hence, AâˆªÂ B = {x:Â xÂ âˆˆÂ N and 1 <Â xÂ < 10}

(v)Â A = {1, 2, 3},Â BÂ =Â Î¦

So the union of the pairs of set can be written as

AâˆªÂ B = {1, 2, 3}

2. Let A = {a,Â b}, B = {a,Â b,Â c}. Is AÂ âŠ‚Â B? What is AÂ âˆªÂ B?

Solution:

It is given that

A = {a,Â b} and B = {a,Â b,Â c}

Yes, AÂ âŠ‚Â B

So the union of the pairs of set can be written as

AâˆªÂ B = {a,Â b,Â c} = B

3. If A and B are two sets such that AÂ âŠ‚Â B, then what is AÂ âˆªÂ B?

Solution:

If A and B are two sets such that AÂ âŠ‚Â B, then AÂ âˆªÂ B = B.

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)Â AÂ âˆªÂ B

(ii)Â AÂ âˆªÂ C

(iii)Â BÂ âˆªÂ C

(iv)Â BÂ âˆªÂ D

(v)Â AÂ âˆªÂ BÂ âˆªÂ C

(vi)Â AÂ âˆªÂ BÂ âˆªÂ D

(vii)Â BÂ âˆªÂ CÂ âˆªÂ 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)Â AÂ âˆªÂ B = {1, 2, 3, 4, 5, 6}

(ii)Â AÂ âˆªÂ C = {1, 2, 3, 4, 5, 6, 7, 8}

(iii)Â BÂ âˆªÂ C = {3, 4, 5, 6, 7, 8}

(iv)Â BÂ âˆªÂ D = {3, 4, 5, 6, 7, 8, 9, 10}

(v)Â AÂ âˆªÂ BÂ âˆªÂ C = {1, 2, 3, 4, 5, 6, 7, 8}

(vi)Â AÂ âˆªÂ BÂ âˆªÂ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(vii) BÂ âˆªÂ CÂ âˆªÂ D = {3, 4, 5, 6, 7, 8, 9, 10}

5. Find the intersection of each pair of sets:

(i)Â X = {1, 3, 5} Y = {1, 2, 3}

(ii)Â A = {a,Â e,Â i,Â o,Â u} B = {a,Â b,Â c}

(iii)Â A = {x:Â xÂ is a natural number and multiple of 3}

B = {x:Â xÂ is a natural number less than 6}

(iv)Â A = {x:Â xÂ is a natural number and 1 <Â xÂ â‰¤Â 6}

B = {x:Â xÂ is a natural number and 6 <Â xÂ < 10}

(v)Â A = {1, 2, 3}, B =Â Î¦

Solution:

(i)Â X = {1, 3, 5}, Y = {1, 2, 3}

So the intersection of the given set can be written as

XÂ âˆ©Â Y = {1, 3}

(ii)Â A = {a,Â e,Â i,Â o,Â u}, B = {a,Â b,Â c}

So the intersection of the given set can be written as

AÂ âˆ©Â B = {a}

(iii)Â A = {x:Â xÂ is a natural number and multiple of 3} = (3, 6, 9 â€¦}

B = {x:Â xÂ is a natural number less than 6} = {1, 2, 3, 4, 5}

So the intersection of the given set can be written as

AÂ âˆ©Â B = {3}

(iv)Â A = {x:Â xÂ is a natural number and 1 <Â xÂ â‰¤Â 6} = {2, 3, 4, 5, 6}

B = {x:Â xÂ is a natural number and 6 <Â xÂ < 10} = {7, 8, 9}

So the intersection of the given set can be written as

AÂ âˆ©Â B =Â Î¦

(v)Â A = {1, 2, 3}, B =Â Î¦

So the intersection of the given set can be written as

AÂ âˆ©Â B =Â Î¦

6. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

(i)Â AÂ âˆ©Â B

(ii)Â BÂ âˆ©Â C

(iii)Â AÂ âˆ©Â CÂ âˆ©Â D

(iv)Â AÂ âˆ©Â C

(v)Â BÂ âˆ©Â D

(vi)Â AÂ âˆ©Â (BÂ âˆªÂ C)

(vii)Â AÂ âˆ©Â D

(viii)Â AÂ âˆ©Â (BÂ âˆªÂ D)

(ix)Â (AÂ âˆ©Â B)Â âˆ©Â (BÂ âˆªÂ C)

(x)Â (AÂ âˆªÂ D)Â âˆ©Â (BÂ âˆªÂ C)

Solution:

(i)Â AÂ âˆ©Â B = {7, 9, 11}

(ii)Â BÂ âˆ©Â C = {11, 13}

(iii)Â AÂ âˆ©Â CÂ âˆ©Â D = {AÂ âˆ©Â C}Â âˆ©Â D

= {11}Â âˆ©Â {15, 17}

=Â Î¦

(iv)Â AÂ âˆ©Â C = {11}

(v)Â BÂ âˆ©Â D =Â Î¦

(vi)Â AÂ âˆ©Â (BÂ âˆªÂ C) = (AÂ âˆ©Â B)Â âˆªÂ (AÂ âˆ©Â C)

= {7, 9, 11}Â âˆªÂ {11}

= {7, 9, 11}

(vii)Â AÂ âˆ©Â D =Â Î¦

(viii)Â AÂ âˆ©Â (BÂ âˆªÂ D) = (AÂ âˆ©Â B)Â âˆªÂ (AÂ âˆ©Â D)

= {7, 9, 11}Â âˆªÂ Î¦

= {7, 9, 11}

(ix)Â (AÂ âˆ©Â B)Â âˆ©Â (BÂ âˆªÂ C) = {7, 9, 11}Â âˆ©Â {7, 9, 11, 13, 15}

= {7, 9, 11}

(x)Â (AÂ âˆªÂ D)Â âˆ©Â (BÂ âˆªÂ C) = {3, 5, 7, 9, 11, 15, 17)Â âˆ©Â {7, 9, 11, 13, 15}

= {7, 9, 11, 15}

7. If A = {x:Â xÂ is a natural number}, B ={x:Â xÂ is an even natural number}

C = {x:Â xÂ is an odd natural number} and D = {x:Â xÂ is a prime number}, find

(i)Â AÂ âˆ©Â B

(ii)Â AÂ âˆ©Â C

(iii)Â AÂ âˆ©Â D

(iv)Â BÂ âˆ©Â C

(v)Â BÂ âˆ©Â D

(vi)Â CÂ âˆ©Â D

Solution:

It can be written as

A = {x:Â xÂ is a natural number} = {1, 2, 3, 4, 5 â€¦}

B ={x:Â xÂ is an even natural number} = {2, 4, 6, 8 â€¦}

C = {x:Â xÂ is an odd natural number} = {1, 3, 5, 7, 9 â€¦}

D = {x:Â xÂ is a prime number} = {2, 3, 5, 7 â€¦}

(i)Â AÂ âˆ©B = {x:Â xÂ is a even natural number} = B

(ii)Â AÂ âˆ©Â C = {x:Â xÂ is an odd natural number} = C

(iii)Â AÂ âˆ©Â D = {x:Â xÂ is a prime number} = D

(iv)Â BÂ âˆ©Â C =Â Î¦

(v)Â BÂ âˆ©Â D = {2}

(vi)Â CÂ âˆ©Â D = {x:Â xÂ is odd prime number}

8. Which of the following pairs of sets are disjoint?

(i)Â {1, 2, 3, 4} and {x:Â xÂ is a natural number and 4Â â‰¤Â xÂ â‰¤Â 6}

(ii)Â {a,Â e,Â i,Â o,Â u}and {c,Â d,Â e,Â f}

(iii)Â {x:Â xÂ is an even integer} and {x: xÂ is an odd integer}

Solution:

(i)Â {1, 2, 3, 4}

{x:Â xÂ is a natural number and 4Â â‰¤Â xÂ â‰¤Â 6} = {4, 5, 6}

So we get

{1, 2, 3, 4}Â âˆ©Â {4, 5, 6} = {4}

Hence, this pair of sets is not disjoint.

(ii)Â {a,Â e,Â i,Â o,Â u}Â âˆ©Â (c,Â d,Â e,Â f} = {e}

Hence, {a,Â e,Â i,Â o,Â u} and (c,Â d,Â e,Â f} are not disjoint.

(iii)Â {x:Â xÂ is an even integer}Â âˆ©Â {x:Â xÂ is an odd integer} =Â Î¦

Hence, this pair of sets is disjoint.

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)Â A â€“ B

(ii)Â A â€“ C

(iii)Â A â€“ D

(iv)Â B â€“ A

(v)Â C â€“ A

(vi)Â D â€“ A

(vii)Â B â€“ C

(viii)Â B â€“ D

(ix)Â C â€“ B

(x)Â D â€“ B

(xi)Â C â€“ D

(xii)Â D â€“ C

Solution:

(i)Â A â€“ B = {3, 6, 9, 15, 18, 21}

(ii)Â A â€“ C = {3, 9, 15, 18, 21}

(iii)Â A â€“ D = {3, 6, 9, 12, 18, 21}

(iv)Â B â€“ A = {4, 8, 16, 20}

(v)Â C â€“ A = {2, 4, 8, 10, 14, 16}

(vi)Â D â€“ A = {5, 10, 20}

(vii)Â B â€“ C = {20}

(viii)Â B â€“ D = {4, 8, 12, 16}

(ix)Â C â€“ B = {2, 6, 10, 14}

(x)Â D â€“ B = {5, 10, 15}

(xi)Â C â€“ D = {2, 4, 6, 8, 12, 14, 16}

(xii)Â D â€“ C = {5, 15, 20}

10. If X = {a,Â b,Â c,Â d} and Y = {f,Â b,Â d, g}, find

(i)Â X â€“ Y

(ii)Â Y â€“ X

(iii)Â XÂ âˆ©Â Y

Solution:

(i)Â X â€“ Y = {a,Â c}

(ii)Â Y â€“ X = {f,Â g}

(iii)Â XÂ âˆ©Â Y = {b,Â d}

11. IfÂ RÂ is the set of real numbers andÂ QÂ is the set of rational numbers, then what isÂ RÂ â€“Â Q?

Solution:

We know that

R â€“ Set of real numbers

Q â€“ Set of rational numbers

Hence, R â€“ Q is a set of irrational numbers.

12. State whether each of the following statement is true or false. Justify your answer.

(i)Â {2, 3, 4, 5} and {3, 6} are disjoint sets.

(ii)Â {a,Â e,Â i,Â o,Â uÂ } and {a,Â b,Â c,Â d} are disjoint sets.

(iii)Â {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.

(iv)Â {2, 6, 10} and {3, 7, 11} are disjoint sets.
Solution:

(i)Â False

If 3Â âˆˆÂ {2, 3, 4, 5}, 3Â âˆˆÂ {3, 6}

So we get {2, 3, 4, 5}Â âˆ©Â {3, 6} = {3}

(ii)Â False

If aÂ âˆˆÂ {a,Â e,Â i,Â o,Â u},Â aÂ âˆˆÂ {a,Â b,Â c,Â d}

So we get {a,Â e,Â i,Â o,Â u}Â âˆ©Â {a,Â b,Â c,Â d} = {a}

(iii)Â True

Here {2, 6, 10, 14}Â âˆ©Â {3, 7, 11, 15} =Â Î¦

(iv)Â True

Here {2, 6, 10}Â âˆ©Â {3, 7, 11} =Â Î¦

### Access Other Exercise Solutions of Class 11 Maths Chapter 1 â€“ Sets

The links to other exercises in NCERT Class 11 Maths Solutions Chapter 1 are as follows.

Exercise 1.1 Solutions 6 Questions

Exercise 1.2 Solutions 6 Questions

Exercise 1.3 Solutions 9 Questions

Exercise 1.5 Solutions 7 Questions

Exercise 1.6 Solutions 8 Questions

Miscellaneous Exercise On Chapter 1 Solutions 16 Questions