Sets Class 8 RS Aggarwal Exe-5C Goyal Brothers ICSE Maths Solutions Ch-5. We provide step by step Solutions of SETS to develop skill and confidence. In this articles you would learn Operation on sets. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.
Sets Class 8 RS Aggarwal Exe-5C Goyal Brothers ICSE Maths Solutions
| Board | ICSE |
| Subject | Maths |
| Class | 8th |
| writer | RS Aggarwal |
| Book Name | Foundation |
| Ch-5 | Sets |
| Exe-5C | Operation on Sets |
| Edition | 2024-2025 |
Operation on Sets
major types of operations performed on sets, such as: Union of sets (∪) Intersection of sets (∩) Difference of sets ( – ) etc.
Exercise- 5C
Sets Class 8 RS Aggarwal Goyal Brothers ICSE Maths Solutions Ch-5
Page- 78, 79
Que-1: Let A = {a,b,c,d}, B = {b,c,e} and C = {a,b,e}. Find :
(i) A∪B (ii) B∪C (iii) A∪C (iv) A∩B (v) B∩C (vi) A∩C
Solution- (i) {a,b,c,d,e}
(ii) {a,b,c,e}
(iii) {a,b,c,d,e}
(iv) {b,c}
(v) {b,e}
(vi) {a,b}
Que-2: Let A – {2,3,4,6}, B = {5,7,8} and C = {2,7,8,9}. Find :
(i) A∪B (ii) B∪C (iii) A∪C (iv) A∩B (v) B∩C (vi) A∩C
Solution- (i) A∪B = {2,3,4,5,6,7,8}
(ii) B∪C = {2,5,7,8,9}
(iii) A∪C = {2,3,4,6,7,8,9}
(iv) A∩B = ø
(v) B∩C = {7,8}
(vi) A∩C = {2}
Que-3: Let A = {1,4,7,8} and B = {4,6,8,9}. Find (i) A-B (ii) B-A
Solution- (i) A-B = {1,7}
(ii) B-A = {6,9}
Que-4: Let U = {13,14,15,16,17,18,19,20,21}, A = {13,17,19} and B = {14,16,18,20}. Find (i) A’ (ii) B’
Solution- (i) A’ = {14,15,16,18,20,21}
(ii) B’ = {13,15,17,19,21}
Que-5: Let U = {x | x∈Z, -4≤x≤4}, A = {x | x∈W, x<4} and B = {x | x∈N, 2≤x≤4}. Find : (i) A’ (ii) B’
Solution- U = {-4,-3,-2,-1,0,1,2,3,4}
A = {0,1,2,3}
B = {-4,-3,-2,-1,0,1,2}
(i) A’ = {-4,-3,-2,-1,4}
(ii) B’ = {-4,-3,-2,-1,0,1,2}
Que-6: Let U = {x | x∈N, x is a factor of 144}, A = {x | x∈N, x is a factor of 24}, B = {x | x∈N, x is a factor of 36}, C = {x | x∈N, x is a factor of 48}. Find :
(i) A’ (ii) B’ (iii) C’ (iv) A∪B (v) B∪C (vi) A∪C (vii) A∩B’ (viii) B∩C’ (ix) C-A (x) A-(B∩C)
Solution- U = {1,2,3,4,6,9,12,16,18,20,36,48,72,144}
A = {1,2,3,4,6,8,12,24}
B = {1,2,3,4,6,9,12,18,36}
C = {1,2,3,4,6,8,12,16,24,48}
(i) A’ = {9,16,18,36,48,72,144}
(ii) B’ = {8,16,24,48,72,144}
(iii) C’ = {9,18,36,72,144}
(iv) A∪B = {1,2,3,4,6,8,9,12,18,24,36}
(v) B∪C = {1,2,3,4,6,8,12,16,18,24,36,48}
(vi) A∪C = {1,2,3,4,6,8,12,16,24,48}
(vii) A∩B = {8,24}
(viii) B∩C = {9,18,36}
(ix) C-A = {16,48}
(x) A-(B∩C) = A-{1,2,3,4,6,12} = {8,24}
Que-7: Considering the set given in Q6, state whether each of the following statements is true or false :
(i) A∩(B∪C) = A (ii) A⊂C (iii) B⊆C (iv) A∩C’ = ø
Solution- U = {1,2,3,4,6,9,12,16,18,20,36,48,72,144}
A = {1,2,3,4,6,8,12,24}
B = {1,2,3,4,6,9,12,18,36}
C = {1,2,3,4,6,8,12,16,24,48}
(i) A∩(B∪C) = A∩{1,2,3,4,6,8,12,16,18,24,36,48}
= {1,2,3,4,6,8,12,24} = which is A.
(ii) A⊂C is also true.
(iii) B⊆C = it is not true as B is not subset of C.
(iv) A∩C’ = ø
= {1,2,3,4,6,8,12,24}∩{9,18,36,72,144} = ø
it is true.
Que-8: Let A = {a,b,c,d,e}, B = {a,c,e,g} and C = {b,e,f,g}. Then verify the following identities :
(i) B∪C = C∪B (ii) B∩C = C∩B (iii) A∪(B∪C) = (A∪B)∪C (iv) A∩(B∩C) = (A∩B)∩C (v) A∪(B∩C) = (A∪B)∩(A∩C) (vi) A∩(B∪C) = (A∩B)∪(A∩C)
Solution- (i) B∪C = C∪B
{a,b,c,e,f,g} = {a,b,c,e,f,g}
From we get, B∪C = C∪B
(ii) B∩C = C∩B
{e,g} = {e,g}
From we get, B∩C = C∩B
(iii) A∪(B∪C) = (A∪B)∪C
(B∪C) = {a,b,c,e,f,g}
A∪(B∩C) = {a,b,c,e,f,g} ………..(i)
(A∪B) = {a,b,c,d,e,g}
(A∪B)∪C = {a,b,c,d,e,g} ……………..(ii)
From (i) and (ii) we get
A∪(B∪C) = (A∪B)∪C
(iv) A∩(B∩C) = (A∩B)∩C
B∩C = {e,g}, (A∩B)∩C = {e}
A∩B = {a,c,e}, (A∩B)∩C = {e}
From the above relation we get,
A∩(B∩C) = (A∩B)∩C
(v) A∪(B∩C) = (A∪B)∩(A∩C)
B∩C = {e,g}
A∪(B∩C) = {a,b,c,d,e,g}
A∪B = {a,b,c,d,e,g}
A∪C = {a,b,c,d,e,f,g}
(A∪B)∩(A∪C) = {a,b,c,d,e,g}
From above relation we get,
A∪(B∩C) = (A∪B)∩(A∩C)
(vi) A∩(B∪C) = (A∩B)∪(A∩C)
B∪C = {a,b,c,e,f,g}
A∩(B∪C) = {a,b,c,e}
(A∩B)∪(A∩C) = {a,b,c,e}
From above relation we get,
A∩(B∪C) = (A∩B)∪(A∩C).
Que-9: Let A = {b,c,d,e} and B = {d,e,f,g} be two subset of universal set U = {b,c,d,e,f,g}. Then verify the following : (i) (A∪B)’ = (A’∩B’) (ii) (A∩B) = (A’∪B’)
Solution- (i) (A∪B)’ = (A’∩B’)
A∪B = {b,c,d,e,f,g}
(A∪B)’ = { } = ø ……….(i)
A’ = {f,g}, B’ = {b,c}
A’∩B’ = { } = ø ………..(ii)
From (i) and (ii) we get,
(A∪B)’ = (A’∩B’).
(ii) (A∩B) = (A’∪B’)
(A∩B) = {d,e}
(A∩B)’ = {b,c,f,g} ………….(i)
A’ = {f,g}, B’ = {b,c}
(A’∪B’) = {b,c,f,g} ………….(ii)
From (i) and (ii) we get,
(A∩B) = (A’∪B’).
Que-10: Fill in the blanks :
(i) A∪A = …… (ii) A∩A = …… (iii) A∪ø = ……… (iv) A∩ø = ……. (v) (A∪B)’ = ….. (vi) (A∩B)’ = …….
Solution- (i) A
(ii) A
(iii) A
(iv) ø
(v) (A’∩B’)
(vi) (A’∪B’)
Que-11: Let U = {x | x∈N, 4≤x<18} and A,B,C be subsets of U given by A = {x | x is a multiple of 2}, B = {x | x is a multiple of 3} and C = {x | x∈N, x<11}. Then, verify the following :
(i) (A∪B)’ = (A’∩B’) (ii) (A∩B)’ = (A’∪B’) (iii) A-B = A∩B’ (iv) A∪(B∩C) = (A∪B)∩(A∪C)
Solution- U = {4,5,6,7,8,………,17}
A = {2,4,6,8,10,12,14,16,17}
B = {3,6,9,12,15}
C = {1,2,3,4,5,6,7,8,9,10}
(i) (A∪B)’ = (A’∩B’)
A∪B = {4,6,8,9,10,12,14,15,16}
(A∪B)’ = {5,7,11,13,17} …………(i)
A’ = {5,7,9,11,13,15,17}
B’ = {4,5,7,8,10,11,13,14,16,17}
A’∩B’ = {5,7,11,13,17} …………..(ii)
From (i) and (ii) we get,
(A∪B)’ = (A’∩B’)
(ii) (A∩B)’ = (A’∪B’)
(A∩B) = {6,12}
(A∩B)’ = {4,5,7,8,9,10,11,13,14,15,16,17} ……….(i)
A’ = {5,7,9,11,13,15,17}
B’ = {4,5,7,8,10,11,13,14,16,17}
A’∪B’ = {4,5,7,8,9,10,11,13,14,15,16,17} ………….(ii)
From (i) and (ii) we get,
(A∩B)’ = (A’∪B’)
(iii) A-B = A∩B’
A-B = {4,8,10,14,16} ……….(i)
B’ = {4,5,7,8,10,11,13,14,16,17}
A∩B’ = {4,8,10,14,16} ……..(ii)
From (i) and (ii) we get,
A-B = A∩B’
(iv) A∪(B∩C) = (A∪B)∩(A∪C)
B∩C = {6,9}
A∪(B∩C) = {4,6,8,9,10,12,14,16} …………….(i)
A∪B = {4,6,8,9,10,12,14,15,16}
A∪C = {1,2,3,4,5,6,7,8,9,10,11,12,14,16}
(A∪B)∩(A∪C) = {4,6,8,9,10,12,14,16} ………………..(ii)
From (i) and (ii) we get,
A∪(B∩C) = (A∪B)∩(A∪C).
— : End of Sets Class 8 RS Aggarwal Exe-5C Goyal Brothers Prakashan ICSE :–
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