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
From Problems on Union of Sets to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 13, 24 05:12 PM
Apr 13, 24 03:29 PM
Apr 13, 24 01:27 PM
Apr 13, 24 12:41 PM
Apr 12, 24 04:22 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.