NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5
Ex 1.5 Class 11 Maths Question 1.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = (2, 4, 6, 8} and C = {3, 4, 5, 6}. Find(i) A’
(ii) B’
(iii) (A ∪ C)’
(iv) (A ∪ B)’
(v) (A’)’
(vi) (B – C)’
Solution.
Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C
= {3, 4, 5, 6}
(i) A’= U – A
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4}
= {5, 6, 7, 8, 9}
(ii) B’ = U – B
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 4, 6, 8}
= {1, 3, 5, 7, 9}
(iii) A ∪ C = {1, 2, 3, 4} ∪ {3, 4, 5, 6}
= (1, 2, 3, 4, 5, 6}
(A ∪ C)’ = U – (A ∪ C)
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4, 5, 6}
= {7, 8, 9}
(iv) A ∪ B = {1, 2, 3, 4} ∪ {2, 4, 6, 8}
= {1, 2, 3, 4, 6, 8}
(A ∪ B)’ = U – (A ∪ B)
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4, 6, 8}
= {5, 7, 9}
(v) We know that A’ = {5, 6, 7, 8, 9}
(A’)’ = U – A’
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {5, 6, 7, 8, 9}
= {1, 2, 3, 4}
(vi) B – C = {2, 4, 6, 8} – {3, 4, 5, 6}
= {2, 8}
(B – C)’ = U – (B – C)
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 8}
= {1, 3, 4, 5, 6, 7, 9}.
Ex 1.5 Class 11 Maths Question 2.
If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}
Solution.
(i) A’
= U – A = {a, b, c, d, e, f, g, h} – {a, b, c}
= {d, e, f, g, h}
(ii) B’ = U – B = {a, b, c, d, e, f, g,
h} – {d, e, f, g}
= {a, b, c, h}
(iii) C’ = U – C = {a, b, c, d, e, f, g,
h} – {a, c, e, g}
= {b, d, f, h}
(iv) D’ = U – D = {a, b, c, d, e, f, g,
h} – {f, g, h, a}
= {b, c, d, e}
Ex 1.5 Class 11 Maths Question 3.
Taking the set of natural numbers as the universal set, write down the complements of the following sets:(i) {x: x is an even natural number}
(ii) {x: x is an odd natural number}
(iii) {x: x is a positive multiple of 3}
(iv) {x: x is a prime number}
(v) {x: x is a natural number divisible by 3 and 5}
(vi) {x: x is a perfect square}
(vii) {x: x is a perfect cube}
(viii) {x: x + 5 = 8}
(ix) (x: 2x + 5 = 9)
(x) {x: x ≥ 7}
(xi) {x: x ∈ W and 2x + 1 > 10}
Solution.
Ex 1.5 Class 11 Maths Question 4.
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that(i) (A ∪ B)’ = A’ ∩ B’
(ii) (A ∩ B)’ = A’ ∪ B’
Solution.
Ex 1.5 Class 11 Maths Question 5.
Draw appropriate Venn diagram for each of the following:(i) (A ∪ B)’
(ii) A’ ∩ B’
(iii) (A ∩ B)’
(iv) A’ ∪ B’
Solution.
Ex 1.5 Class 11 Maths Question 6.
Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A’?Solution.
Here U = {x: x is a triangle}
A = {x: x is a triangle and has at least one angle different from 60°}
∴ A’ = U – A = {x: x is a triangle} – {x:
x is a triangle and has at least one angle different from 60°}
= {x: x is a triangle and has all angles equal to 60°}
= {x: x is an equilateral triangle}
Ex 1.5 Class 11 Maths Question 7.
Fill in the blanks to make each of the following a true statement:(i) A ∪ A’ = …….
(ii) φ’ ∩ A = …….
(iii) A ∩ A’ = …….
(iv) U’ ∩ A = …….
Solution.
(i) A
∪ A’= U
(ii) φ’
∩ A = U ∩ A = A
(iii) A
∩ A’ = φ
(iv) U’
∩ A = φ ∩ A = φ
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