**NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4**

**Ex 1.4 Class 11 Maths 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 ≤ 6};

B = (x: x is a natural number and 6 < x < 10}

**(v)** A = {1, 2, 3}, B = Ï†

**Solution.**

**Ex 1.4 Class 11
Maths Question 2.**

Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

**Solution.**

Here A = {a, b} and B = {a, b, c}. All elements of set A are present in set B.

∴ A ⊂ B. Now, A ∪ B = {a, b, c) = B.

**Ex 1.4 Class 11
Maths Question 3.**

If A and B are two sets such that A ⊂ B, then what is A ∪ B?

**Solution.**

Given A and B are two sets such that A ⊂ B.

Take A = {1, 2} and B = {1, 2, 3}.

A ∪ B = {1, 2, 3) = B.

**Ex 1.4 Class
11 Maths 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**

**(i)****(ii)**A ∪ C

**(iii)**B ∪ C

**(iv)**B ∪ D

**(v)**A ∪ B ∪ C

**(vi)**A ∪ B ∪ D

**(vii)**B ∪ C ∪ D

**Solution.**

Here A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5,
6, 7, 8} and D = {7, 8, 9, 10}

**Ex 1.4 Class 11
Maths Question 5.**

Find
the intersection of each pair of sets.**X = {1 ,3, 5}, Y = {1, 2, 3}**

**(i)****(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 ≤ 6};

B = (x: x is a natural number
and 6 < x < 10}

**(v)** A
= {1, 2, 3}, B = Ï†

**Solution.**

**(i)** Here
X = {1, 3, 5} and Y = {1, 2, 3}

∴ X ∩ Y = {1, 3}

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

∴ A ∩ B = {a}

**(iii)** Here A = {x: x is a natural number
and multiple of 3} = {3, 6, 9, 12, ….} and B = {x: x is a natural number less
than 6} = {1, 2, 3, 4, 5}

∴ A ∩ B = {3}

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

∴ A ∩ B = Ï†

**(v)** Here A = {1, 2, 3) and B = Ï†

∴ A ∩ B = Ï†

**Ex 1.4 Class 11
Maths 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**

**(i)****(ii)**B ∩ C

**(iii)**A ∩ C ∩ D

**(iv)**A ∩ C

**(v)**B ∩ D

**(vi)**A ∩ (B ∪ C)

**(vii)**A ∩ D

**(viii)**A ∩ (B ∪ D)

**(ix)**(A ∪ B) ∩ (B ∪ C)

**(x)**(A ∪ D) ∩ (B ∪ C)

**Solution.**

Here A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15,
17}

**Ex 1.4 Class 11
Maths 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**

**(i)****(ii)**A ∩ C

**(iii)**A ∩ D

**(iv)**B ∩ C

**(v)**B ∩ D

**(vi)**C ∩ D

**Solution.**

Here A = {x: x is a natural number} = {1, 2, 3, 4, 5, …….}

B = {x: x is an even natural number} = {2, 4, 6, 8, 10, ………}

C = {x: x is an odd natural number} = {1, 3, 5, 7, 9, ………}

and D = {x: x is a prime number} = {2, 3, 5, 7, 11, ……..}

**(i)** A ∩ B = {x: x is a natural number}
∩ {x: x is an even natural number}

= {x: x is an even natural number} = B.

**(ii)** A ∩ C = {x: x is a natural number}
∩ {x: x is an odd natural number}

= {x: x is an odd natural number} = C.

**(iii)** A ∩ D = {x: x is a natural number}
∩ {x: x is a prime number}

= {x: x is a prime number} = D.

**(iv)** B ∩ C = {x: x is an even natural
number} ∩ {x: x is an odd natural number} = Ï†.

**(v)** B ∩ D = [x: x is an even natural
number} ∩ {x: x is a prime number} = {2}.

**(vi)** C ∩ D = {x: x is an odd natural
number} ∩ {x: x is a prime number} = {x: x is an odd prime number}.

**Ex 1.4 Class 11
Maths 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}**

**(i)****(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)** Let
A = {1, 2, 3, 4}

and B = {x: x is a natural number and 4 ≤ x ≤ 6} = {4, 5, 6}

∴ A ∩ B = {1, 2, 3, 4} ∩ {4, 5, 6} = {4}

Hence, A and B are not disjoint sets.

**(ii)** Let A = {a, e, i, o, u} and B = {c,
d, e, f}

∴ A ∩ B = {e}

Hence, A and B are not disjoint sets.

**(iii)** Let A = {x: x is an even integer}
and B = {x: x is an odd integer}

∴ A ∩ B = Ï†. Hence, A and B are disjoint
sets.

**Ex 1.4 Class 11
Maths 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} and D = {5, 10, 15, 20}; find**A – B**

**(i)****(ii)**A – C

**(iii)**A – D

**(iv)**B – A

**(v)**C – A

**(vi)**D – A

**(vii)**B – C

**(viii)**B – D

**(ix)**C – B

**(x)**D – B

**(xi)**C – D

**(xii)**D – C

**Solution.**

Here 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}

**(i)** A
– B = {3, 6, 9, 12, 15, 18, 21} – {4, 8, 12, 16, 20} = {3, 6, 9, 15, 18, 21}

**(ii)** A
– C = {3, 6, 9, 12, 15, 18, 21} – {2, 4, 6, 8, 10, 12, 14, 16} = {3, 9, 15, 18,
21}

**(iii)** A
– D = {3, 6, 9, 12, 15, 18, 21} – {5, 10, 15, 20} = {3, 6, 9, 12, 18, 21}

**(iv)** B
– A = {4, 8, 12, 16, 20} – {3, 6, 9, 12, 15, 18, 21} = {4, 8, 16, 20}

**(v)** C
– A = {2, 4, 6, 8, 10, 12, 14, 16} – {3, 6, 9, 12, 15, 18, 21} = {2, 4, 8, 10,
14, 16}

**(vi)** D
– A = {5, 10, 15, 20} – {3, 6, 9, 12, 15, 18, 21} = {5, 10, 20}

**(vii)** B
– C = {4, 8, 12, 16, 20} – {2, 4, 6, 8, 10, 12, 14, 16} = {20}

**(viii)** B
– D = {4, 8, 12, 16, 20} – {5, 10, 15, 20} = {4, 8, 12, 16}

**(ix)** C
– B = {2, 4, 6, 8, 10, 12, 14, 16} – {4, 8, 12, 16, 20} = {2, 6, 10, 14}

**(x)** D
– B = {5, 10, 15, 20} – {4, 8, 12, 16, 20} = {5, 10, 15}

**(xi)** C
– D = {2, 4, 6, 8, 10, 12, 14, 16} – {5, 10, 15, 20} = {2, 4, 6, 8, 12, 14, 16}

**(xii)** D
– C = {5, 10, 15, 20} – {2, 4, 6, 8, 10, 12, 14, 16} = {5, 15, 20}

**Ex 1.4 Class 11
Maths Question 10.**

If
X = {a, b, c, d} and Y = {f, b, d, g}, find**X – Y**

**(i)****(ii)**Y – X

**(iii)**X ∩ Y

**Solution.**

Here X = {a, b, c, d} and Y = {f, b, d, g}

**(i)** X
– Y = {a, b, c, d} – {f, b, d, g} = {a, c}

**(ii)** Y
– X = {f, b, d, g} – {a, b, c, d} = {f, g}

**(iii)** X
∩ Y = {a, b, c, d} ∩ {f, b, d, g} = {b, d}

**Ex 1.4 Class 11
Maths Question 11.**

If R is the set of real numbers and Q is the set of rational numbers, then what
is R – Q?

**Solution.**

We know that set of real numbers contain rational and irrational numbers. So R
– Q = set of irrational numbers.

**Ex 1.4 Class 11
Maths Question 12.**

State
whether each of the following statements 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.**

**Related Links:**

**NCERT Solutions for Maths Class 9**