CBSE Class 8 > Class 8 Notes > ML Aggarwal: Operation on Sets Venn Diagram - 2
ML Aggarwal: Operation on Sets Venn Diagram - 2
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Page 1
1. From the adjoining Venn diagram, find the following sets :
(i) A
(ii) B
(iii) ?
(iv) A’
(v) B’
(vi) A ? B
(vii) A n B
(viii) (A ? B)’
(ix) (A n B)’
Solution:-
From the Venn diagram,
(i) A = {0, 5, 7, 8, 9, 11}
(ii) B = {2, 5, 6, 8}
(iii) ? = {0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12}
(iv) A’
We know that A’ = ? – A
So, A’ = {1, 2, 4, 6, 12}
Page 2
1. From the adjoining Venn diagram, find the following sets :
(i) A
(ii) B
(iii) ?
(iv) A’
(v) B’
(vi) A ? B
(vii) A n B
(viii) (A ? B)’
(ix) (A n B)’
Solution:-
From the Venn diagram,
(i) A = {0, 5, 7, 8, 9, 11}
(ii) B = {2, 5, 6, 8}
(iii) ? = {0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12}
(iv) A’
We know that A’ = ? – A
So, A’ = {1, 2, 4, 6, 12}
(v) B’
We know that B’ = ? – B
So, B’ = {0, 1, 4, 7, 9, 11, 12}
(vi) A ? B = {0, 2 , 5, 6, 7, 8, 9, 11}
(vii) A n B = {5, 8}
(viii) (A ? B)’ = {1, 4, 12}
(ix) (A n B)’ = {0, 1, 2, 4, 6, 7, 9, 11, 12}
2. From the adjoining Venn diagram, find the following sets:
(i) P
(ii) Q
(iii) ?
(iv) P’
(v) Q’
(vi) P ? Q
(vii) P n Q
(viii) (P ? Q)’
(ix) (P n Q)’
Solution:-
From the given Venn diagram, we have,
Page 3
1. From the adjoining Venn diagram, find the following sets :
(i) A
(ii) B
(iii) ?
(iv) A’
(v) B’
(vi) A ? B
(vii) A n B
(viii) (A ? B)’
(ix) (A n B)’
Solution:-
From the Venn diagram,
(i) A = {0, 5, 7, 8, 9, 11}
(ii) B = {2, 5, 6, 8}
(iii) ? = {0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12}
(iv) A’
We know that A’ = ? – A
So, A’ = {1, 2, 4, 6, 12}
(v) B’
We know that B’ = ? – B
So, B’ = {0, 1, 4, 7, 9, 11, 12}
(vi) A ? B = {0, 2 , 5, 6, 7, 8, 9, 11}
(vii) A n B = {5, 8}
(viii) (A ? B)’ = {1, 4, 12}
(ix) (A n B)’ = {0, 1, 2, 4, 6, 7, 9, 11, 12}
2. From the adjoining Venn diagram, find the following sets:
(i) P
(ii) Q
(iii) ?
(iv) P’
(v) Q’
(vi) P ? Q
(vii) P n Q
(viii) (P ? Q)’
(ix) (P n Q)’
Solution:-
From the given Venn diagram, we have,
(i) P = {a, b, d, e, f, g, h, i}
(ii) Q = {b, d, e}
(iii) ? = {a, b, c, d, e, f, g, h, i, j}
(iv) P’ = {c, j}
(v) Q’ = {a, c, f, g, h, i, j}
(vi) P ? Q = {a, b, d, e, f, g, h, i}
(vii) P n Q = {b, d, e}
(viii) (P ? Q)’ = {c, j}
(ix) (P n Q)’ = {a, c, f, g, h, i, j}
3. From the adjoining Venn diagram, find the following sets :
(i) ?
(ii) A n B
(iii) A n B n C
(iv) C’
(v) A – C
(vi) B – C
(vii) C – B
(viii) (A ? B)’
(ix) (A ? B ? C)’
Page 4
1. From the adjoining Venn diagram, find the following sets :
(i) A
(ii) B
(iii) ?
(iv) A’
(v) B’
(vi) A ? B
(vii) A n B
(viii) (A ? B)’
(ix) (A n B)’
Solution:-
From the Venn diagram,
(i) A = {0, 5, 7, 8, 9, 11}
(ii) B = {2, 5, 6, 8}
(iii) ? = {0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12}
(iv) A’
We know that A’ = ? – A
So, A’ = {1, 2, 4, 6, 12}
(v) B’
We know that B’ = ? – B
So, B’ = {0, 1, 4, 7, 9, 11, 12}
(vi) A ? B = {0, 2 , 5, 6, 7, 8, 9, 11}
(vii) A n B = {5, 8}
(viii) (A ? B)’ = {1, 4, 12}
(ix) (A n B)’ = {0, 1, 2, 4, 6, 7, 9, 11, 12}
2. From the adjoining Venn diagram, find the following sets:
(i) P
(ii) Q
(iii) ?
(iv) P’
(v) Q’
(vi) P ? Q
(vii) P n Q
(viii) (P ? Q)’
(ix) (P n Q)’
Solution:-
From the given Venn diagram, we have,
(i) P = {a, b, d, e, f, g, h, i}
(ii) Q = {b, d, e}
(iii) ? = {a, b, c, d, e, f, g, h, i, j}
(iv) P’ = {c, j}
(v) Q’ = {a, c, f, g, h, i, j}
(vi) P ? Q = {a, b, d, e, f, g, h, i}
(vii) P n Q = {b, d, e}
(viii) (P ? Q)’ = {c, j}
(ix) (P n Q)’ = {a, c, f, g, h, i, j}
3. From the adjoining Venn diagram, find the following sets :
(i) ?
(ii) A n B
(iii) A n B n C
(iv) C’
(v) A – C
(vi) B – C
(vii) C – B
(viii) (A ? B)’
(ix) (A ? B ? C)’
Solution:-
From the Venn diagram,
A = {0, 3, 5, 8, 10}
B = {0, 1, 5, 7, 8, 11}
C = {0, 1, 3, 4, 5, 6}
(i) ? = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
(ii) A n B = {0, 5, 8}
(iii) A n B n C = {0, 5}
(iv) C’
We know that C’ = ? – C
So, C’ = {2, 7, 8, 9, 10, 11, 12}
(v) A – C = {8, 10}
(vi) B – C = {7, 8, 11}
(vii) C – B = {3, 4, 6}
(viii) (A ? B)’ = {2, 4, 6, 9, 12}
(ix) (A ? B ? C)’ = {2, 9, 12}
Page 5
1. From the adjoining Venn diagram, find the following sets :
(i) A
(ii) B
(iii) ?
(iv) A’
(v) B’
(vi) A ? B
(vii) A n B
(viii) (A ? B)’
(ix) (A n B)’
Solution:-
From the Venn diagram,
(i) A = {0, 5, 7, 8, 9, 11}
(ii) B = {2, 5, 6, 8}
(iii) ? = {0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12}
(iv) A’
We know that A’ = ? – A
So, A’ = {1, 2, 4, 6, 12}
(v) B’
We know that B’ = ? – B
So, B’ = {0, 1, 4, 7, 9, 11, 12}
(vi) A ? B = {0, 2 , 5, 6, 7, 8, 9, 11}
(vii) A n B = {5, 8}
(viii) (A ? B)’ = {1, 4, 12}
(ix) (A n B)’ = {0, 1, 2, 4, 6, 7, 9, 11, 12}
2. From the adjoining Venn diagram, find the following sets:
(i) P
(ii) Q
(iii) ?
(iv) P’
(v) Q’
(vi) P ? Q
(vii) P n Q
(viii) (P ? Q)’
(ix) (P n Q)’
Solution:-
From the given Venn diagram, we have,
(i) P = {a, b, d, e, f, g, h, i}
(ii) Q = {b, d, e}
(iii) ? = {a, b, c, d, e, f, g, h, i, j}
(iv) P’ = {c, j}
(v) Q’ = {a, c, f, g, h, i, j}
(vi) P ? Q = {a, b, d, e, f, g, h, i}
(vii) P n Q = {b, d, e}
(viii) (P ? Q)’ = {c, j}
(ix) (P n Q)’ = {a, c, f, g, h, i, j}
3. From the adjoining Venn diagram, find the following sets :
(i) ?
(ii) A n B
(iii) A n B n C
(iv) C’
(v) A – C
(vi) B – C
(vii) C – B
(viii) (A ? B)’
(ix) (A ? B ? C)’
Solution:-
From the Venn diagram,
A = {0, 3, 5, 8, 10}
B = {0, 1, 5, 7, 8, 11}
C = {0, 1, 3, 4, 5, 6}
(i) ? = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
(ii) A n B = {0, 5, 8}
(iii) A n B n C = {0, 5}
(iv) C’
We know that C’ = ? – C
So, C’ = {2, 7, 8, 9, 10, 11, 12}
(v) A – C = {8, 10}
(vi) B – C = {7, 8, 11}
(vii) C – B = {3, 4, 6}
(viii) (A ? B)’ = {2, 4, 6, 9, 12}
(ix) (A ? B ? C)’ = {2, 9, 12}
4. Draw Venn diagrams to show the relationship between the
following pairs of sets:
(i) A = {x | x ? N, x = 2n, n = 5} and B = {x | x ? W, x = 4n, n < 5}
Solution:-
From the question it is given that,
A = {x | x ? N, x = 2n, n = 5}
x = 2n = (2 × 1) = 2 … (2 × 5) = 10
A = {2, 4, 6, 8, 10}
B = {x | x ? W, x = 4n, n < 5}
x = 4n = (4 × 0) = 0 … (4 × 4) = 16
B = {4, 8, 12, 16}
A n B = {4, 8}
Therefore, the sets are overlapping.
An adjoining Venn diagrams to show the relationship between the A and
B sets,
(ii) A = {prime factors of 42} and B = {prime factors of 60}
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Apr 26, 2026 Last updated
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