Problems on Union of Sets

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

Sets Theory

Representation of a Set

Types of Sets

Finite Sets and Infinite Sets

Power Set

Problems on Union of Sets

Problems on Intersection of Sets

Difference of two Sets

Complement of a Set

Problems on Complement of a Set

Problems on Operation on Sets

Word Problems 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

Examples on Venn Diagram



8th Grade Math Practice

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