NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4

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

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4 are the part of NCERT Solutions for Class 11 Maths. In this post, you will find the NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4.

## 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
(i)
A
B
(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.
(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.
(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
(i)
A ∩ B
(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
(i)
A ∩ B
(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?
(i)
{1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 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) 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
(i)
A – B
(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
(i)
X – Y
(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.