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 = φ
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 = φ
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 = φ
(v) Here A = {1, 2, 3) and B = φ
∴ A ∩ B = φ
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} = φ.
(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 = φ. 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.
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