## Sets - NCERT Exercise 1.5 Answers

CBSE Class 11 Maths

Q1: 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)'

(i) A' =  U - A = {5,6,7,8,9}

(ii) B'  = U - B = {1,3,5,7,9}

(iii) (A ∪ C)'
A ∪ C = {1,2,3,4,5,6}
(A ∪ C)' = {7,8,9}

OR
(A ∪ C)' = A' ∩ C'
= {5,6,7,8,9} ∩ {1,2,7,8,9}
= {7,8,9}

(iv) (A ∪ B)'
(A ∪ B) = {1,2,3,4,6,8}
(A ∪ B)' = {5, 7, 9}

(v) (A')'
A' = {5,6,7,8,9}
(A')' = {5,6,7,8,9}'  = { 1, 2, 3, 4}

(vi) (B – C)'
(B - C)' = {2,8}' = {1,3,5,6,7,9}

Q2: 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}

(i) A = {a, b, c}
A' = U - A = {d,e,f,g,h}

(ii) B' = {d, e, f, g}'
= {a, b, c, h}

(iii) C' = {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}

Q3: 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 ∈ N and 2x + 1 > 10 }

Let U = N set of natural numbers

(i) {x : x is an even natural number}
{x : x is an even natural number}' = {x : x is an odd natural number}

(ii) { x : x is an odd natural number }' = {x: x is an even natural number}

(iii) {x : x is a positive multiple of 3} = {x: x ∈ N and x = 3n where n ∈ N }

{x : x is a positive multiple of 3}' = {x: x ∈ N and x is not a multiple of 3}

(iv) { x : x is a prime number }' = {x : x is a positive composite number and x ≠ 1}

(v) {x : x is a natural number divisible by 3 and 5}'
= {x : xisa natural number that is not divisible by 3 or 5}

(vi) { x : x is a perfect square }' = {x : x ∈ N and x is not a perfect square}

(vii) { x : x is a perfect cube}' = {x : x ∈ N and x is not a perfect cube}

(viii) { x : x + 5 = 8 } = {x : x ∈ N and x = 3}
{ x : x + 5 = 8 }' = {x : x ∈ N and x ≠ 3}

(ix) { x : 2x + 5 = 9} = {x : x ∈ N and x = 2}
{ x : 2x + 5 = 9}' = {x : x ∈ N and x ≠ 2}

(x) { x : x ≥ 7 }' = {x : x ∈ N and x < 7}

(xi) { x : x ∈ N and 2x + 1 > 10 }'
= {x : x ∈ N and x ≤ 9/2}

Q4: 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'

Given,
U = {1, 2, 3, 4, 5, 6, 7, 8, 9 },
A = {2, 4, 6, 8} and
B = { 2, 3, 5, 7}
(i)  (A ∪ B)' = {2,3,4,5,6,7,8}' = {1, 9}

A' ∩ B'  = {1,3,5,7,9}' ∩ {1,4,6,8,9}' = {1, 9}

∴ (A ∪ B)' = A' ∩ B'

(ii) (A ∩ B)' = {2}' = {1,3,4,5,6,7,8,9}

A' ∪ B' = {1,3,5,7,9} ∪ {1,4,6,8,9} = {1,3,4,5,6,7,8,9}

∴  (A ∩ B)' = A' ∪ B'

Q5: Draw appropriate Venn diagram for each of the following :
(i) (A ∪ B)',
(ii) A' ∩ B',
(iii) (A ∩ B)',
(iv) A' ∪ B'

(i) (A ∪ B)',

(ii) Since (A ∪ B)' = A' ∩ B',

(iii) (A ∩ B)',

(iv) Since  A' ∪ B' = (A ∩ B)'

Q6: 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'?

Answer: U = {Set of all triangles in a plane}
A = {set of all triangles with at least one angle different from 60°}
A' = U - A = {set of all equilateral triangles}

Q7: Fill in the blanks:
(i) A ∪ A' = . . .
(ii) φ ∩ A = . . .
(iii) A ∩ A' = . . .
(iv) U' ∩ A = . . .

(i) A ∪ A' = U
(ii) φ ∩ A = A
(iii) A ∩ A' = φ
(iv) U' ∩ A = φ

Special Mathematical Constants
SETS (Unit Test Paper)
SETS (VENN DIAGRAMS)
SETS (Operations of Sets)
SETS (NCERT Ex 1.4 Q1-Q5)
SETS (NCERT Ex 1.4 Q6 - Q8)
SETS (NCERT Ex 1.4 Q9 - Q12)
Laws of Set Operations  