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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