Solved problems on union of sets are given below to get a fair idea how to find the union of two or more sets.
We know, the union of two or more sets is a set which contains all the elements in those sets.
Click Here to know more about the operations on union of sets.
Solved problems on union of sets:
1. Let A = {x : x is a natural number and a factor of 18} and B = {x : x is a natural number and less than 6}. Find A ∪ B.
Solution:
A = {1, 2, 3, 6, 9, 18}
B = {1, 2, 3, 4, 5}
Therefore, A ∪ B = {1, 2, 3, 4, 5, 6, 9, 18}
2. Let A = {0, 1, 2, 3, 4, 5}, B = {2, 4, 6, 8} and C = {1, 3, 5, 7}
Verify (A ∪ B) ∪ C = A ∪ (B ∪
C)
Solution:
(A ∪ B) ∪ C = A ∪ (B ∪ C)
L.H.S. = (A ∪ B) ∪ C
A ∪
B = {0, 1, 2, 3, 4, 5, 6, 8}
(A ∪
B) ∪
C = {0, 1, 2, 3, 4, 5, 6, 7, 8} ……………….. (1)
R.H.S. = A ∪ (B ∪ C)
B ∪
C = {1, 2, 3, 4, 5, 6, 7, 8}
A ∪
(B ∪
C) = {0, 1, 2, 3, 4, 5, 6, 7, 8} ……………….. (2)
Therefore, from (1) and (2), we conclude that;
(A ∪
B) ∪
C = A ∪ (B ∪ C) [verified]
More worked-out problems on union of sets to find the union of three sets.
3. Let X = {1, 2, 3, 4}, Y = {2, 3, 5} and Z = {4, 5, 6}.
(i) Verify X ∪ Y = Y ∪ X
(ii) Verify (X ∪ Y) ∪ Z = X ∪ (Y ∪
Z)
Solution:
(i) X ∪ Y
= Y ∪ X
L.H.S = X ∪ Y
= {1, 2, 3, 4} ∪
{2, 3, 4} = {1, 2, 3, 4, 5}
R.H.S. = Y ∪ X
= {2, 3, 5} U {1, 2, 3, 4} = {2, 3, 5, 1, 4}
Therefore, X ∪ Y
= Y ∪ X [verified]
(ii) (X ∪
Y) ∪ Z
= X ∪ (Y
∪ Z)
L.H.S. = (X ∪ Y)
∪ Z
X ∪ Y
= {1, 2, 3, 4} U {2, 3, 5}
= {1, 2, 3, 4, 5}
Now (X ∪ Y)
∪ Z
= {1, 2, 3, 4, 5, 6} {4, 5, 6}
= {1, 2, 3, 4, 5, 6}
R.H.S. = X U (Y ∪
Z)
Y ∪ Z
= {2, 3, 5} ∪
{4, 5, 6}
= {2, 3, 4, 5, 6}
X ∪ (Y
∪ Z)
= {1, 2, 3, 4} ∪
{2, 3, 4, 5, 6}
Therefore, (X ∪
Y) ∪ Z
= X ∪ (Y
∪ Z)
[verified]
● Set Theory
● Finite Sets and Infinite Sets
● Problems on Intersection of Sets
● Problems on Complement of a Set
● Problems on Operation on Sets
● Venn Diagrams in Different Situations
● Relationship in Sets using Venn Diagram
● Union of Sets using Venn Diagram
● Intersection of Sets using Venn Diagram
● Disjoint of Sets using Venn Diagram
● Difference of Sets using Venn Diagram
8th Grade Math Practice
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