CBSE Class 11 Maths Sets - NCERT Exercise 1.5 Answers (#class11Maths)(#eduvictors)

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)'


Answer:
(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}

Answer:
(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 }

Answer:
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'


Answer: 
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'

Answer:
(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 = . . .


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


☞See also:
 Special Mathematical Constants

 SETS (NCERT Ex 1.1)
 SETS (NCERT Ex 1.2)
 Different Types of Sets
 SETS (NCERT Ex 1.3)

 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