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 ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

(ii) Verify A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

**Solution:**

(i) A ∪ (B ∩ C) = (A ∪
B) ∩ (A ∪ C)

L.H.S. = A ∪ (B ∩ C)

B ∩ C = {3}

A ∪
(B ∩ C) = {1, 3, 5} ∪ {3} = {1, 3, 5} ……………….. (1)

R.H.S. = (A ∪ B) ∩ (A ∪ C)

A ∪
B = {1, 3, 5, 6}

A ∪
C = {1, 3, 5, 7}

(A ∪
B) ∩ (A ∪ C) = {1, 3, 5, 6} ∩ {1, 3, 5, 7} = {1, 3, 5}
……………….. (2)

From (1) and (2), we conclude that;

A ∪
(B ∩ C) = A ∪ B ∩ (A ∪ C) [*verified*]

(ii) A ∩ (B ∪ C) = (A ∩ B) ∪
(A ∩ C)

L.H.S. = A ∩ (B ∪ C)

B ∪
C = {1, 3, 5, 6, 7}

A ∩ (B ∪ C) = {1, 3, 5} ∩ {1, 3, 5, 6, 7} = {1, 3, 5}
……………….. (1)

R.H.S. = (A ∩ B) ∪ (A ∩ C)

A ∩ B = {3, 5}

A ∩ C = {1, 3}

(A ∩ B) ∪ (A ∩ C) = {3, 5} ∪ {1, 3} = {1, 3, 5}
……………….. (2)

From (1) and (2), we conclude that;

A ∩ (B ⋃ C) = (A ∩ B) ⋃
(A ∩ 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 ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

(ii) Verify A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

**Solution: **

(i) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

L.H.S. = A ∩ (B ∪ C)

B ∪
C = {b, c, d, e, f, g}

A ∩ (B ∪ C) = {b, d, e} ……………….. (1)

R.H.S. = (A ∩ B) ∪ (A ∩ C)

A ∩ B = {b, e}

A ∩ C = {d, e}

(A ∩ B) ∪ (A ∩ C) = {b, d, e} ……………….. (2)

From (1) and (2), we conclude that;

A ∩ (B ⋃ C) = (A ∩ B) ⋃
(A ∩ C) [*verified*]

(ii) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

L.H.S. = A ∪ (B ∩ C)

B ∩ C = {e, f}

A ∪
(B ∩ C) = {a, b, d, e, f} ……………….. (1)

R.H.S. = (A ∪ B) ∩ (A ∪ C)

A∪B
= {a, b, c, d, e, f}

A∪C
= {a, b, d, e, f, g}

(A ∪
B) ∩ (A ∪ C) = {a, b, d, e, f} ……………….. (2)

From (1) and (2), we conclude that;

A ∪
(B ∩ C) = A ∪ B ∩ (A ∪ C) [*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 Operation on 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.**

## 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.