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Solved problems on operation on sets are given below to get a fair idea how to find the union and intersection of two or more sets.
We know, the union of sets is a set which contains all the elements in those sets and intersection of sets is a set which contains all the elements that are common in those sets.
Click Here to know more about the two basic operations on sets.
Solved problems on operation on sets:
1. If A = {1, 3, 5}, B = {3, 5, 6} and C = {1, 3, 7}
(i) Verify that A βͺ (B β© C) = (A βͺ B) β© (A βͺ C)
(ii) Verify A β© (B βͺ C) = (A β© B) βͺ (A β© C)
Solution:
(i) A βͺ (B β© C) = (A βͺ
B) β© (A βͺ C)
L.H.S. = A βͺ (B β© C)
B β© C = {3}
A βͺ
(B β© C) = {1, 3, 5} βͺ {3} = {1, 3, 5} β¦β¦β¦β¦β¦β¦.. (1)
R.H.S. = (A βͺ B) β© (A βͺ C)
A βͺ
B = {1, 3, 5, 6}
A βͺ
C = {1, 3, 5, 7}
(A βͺ
B) β© (A βͺ C) = {1, 3, 5, 6} β© {1, 3, 5, 7} = {1, 3, 5}
β¦β¦β¦β¦β¦β¦.. (2)
From (1) and (2), we conclude that;
A βͺ
(B β© C) = A βͺ B β© (A βͺ C) [verified]
(ii) A β© (B βͺ C) = (A β© B) βͺ
(A β© C)
L.H.S. = A β© (B βͺ C)
B βͺ
C = {1, 3, 5, 6, 7}
A β© (B βͺ C) = {1, 3, 5} β© {1, 3, 5, 6, 7} = {1, 3, 5}
β¦β¦β¦β¦β¦β¦.. (1)
R.H.S. = (A β© B) βͺ (A β© C)
A β© B = {3, 5}
A β© C = {1, 3}
(A β© B) βͺ (A β© C) = {3, 5} βͺ {1, 3} = {1, 3, 5}
β¦β¦β¦β¦β¦β¦.. (2)
From (1) and (2), we conclude that;
A β© (B β C) = (A β© B) β
(A β© C) [verified]
More worked-out problems on operation on sets to find the union and intersection of three sets.
2. Let A = {a, b, d, e}, B = {b, c, e,
f} and C = {d, e, f, g}
(i) Verify A β© (B βͺ C) = (A β© B) βͺ (A β© C)
(ii) Verify A βͺ (B β© C) = (A βͺ B) β© (A βͺ C)
Solution:
(i) A β© (B βͺ C) = (A β© B) βͺ (A β© C)
L.H.S. = A β© (B βͺ C)
B βͺ
C = {b, c, d, e, f, g}
A β© (B βͺ C) = {b, d, e} β¦β¦β¦β¦β¦β¦.. (1)
R.H.S. = (A β© B) βͺ (A β© C)
A β© B = {b, e}
A β© C = {d, e}
(A β© B) βͺ (A β© C) = {b, d, e} β¦β¦β¦β¦β¦β¦.. (2)
From (1) and (2), we conclude that;
A β© (B β C) = (A β© B) β
(A β© C) [verified]
(ii) A βͺ (B β© C) = (A βͺ B) β© (A βͺ C)
L.H.S. = A βͺ (B β© C)
B β© C = {e, f}
A βͺ
(B β© C) = {a, b, d, e, f} β¦β¦β¦β¦β¦β¦.. (1)
R.H.S. = (A βͺ B) β© (A βͺ C)
AβͺB
= {a, b, c, d, e, f}
AβͺC
= {a, b, d, e, f, g}
(A βͺ
B) β© (A βͺ C) = {a, b, d, e, f} β¦β¦β¦β¦β¦β¦.. (2)
From (1) and (2), we conclude that;
A βͺ
(B β© C) = A βͺ B β© (A βͺ C) [verified]
β Set Theory
β Sets Theory
β Types of Sets
β Finite Sets and Infinite Sets
β Power Set
β Problems on Intersection of Sets
β Problems on Complement of a Set
β Problems on Operation on Sets
β Venn Diagrams in Different Situations
β Relationship in Sets using Venn Diagram
β Union of Sets using Venn Diagram
β Intersection of Sets using Venn Diagram
β Disjoint of Sets using Venn Diagram
β Difference of Sets using Venn Diagram
8th Grade Math Practice
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