# Introduction to operation of set-Edu input

There are four types of set operations.

1. Union of sets.

2. Intersection of set s.

3. Difference of sets.

4. Complement of a set.

**1. Union of Sets:**

If we have two sets A and B, then the union both sets will contain all the elements of set A and B

Example:

A= {a, b, c, d, e}, B= {a, b, c}

AUB= {a, b, c, d, e} U {a, b, c}

AUB= {a, b, c, d, e}

A= {a, b, c, d, e}, B= {a, b, c}

BUA= {a, b, c} U {a, b, c, d, e}

BUA= {a, b, c, d, e}

*The green area shows the AUB and BUA.*

- 2. Intersection of Sets
- Frequently Asked Question-FAQs
- What are Set Operations in Set Theory?
- What are the Different Set Operations?
- Which of the Set Operations are Commutative and not Commutative?
- How do you Solve Set Operations Problems?
- What are the Set Operations Symbols?
- How do you Find the Difference Between the Two Sets?
- What are the Union and Intersection operations of Sets?
- How do you Find the Complement of a Set?
- How Do We Use Set Operations in Real Life?

**2. Intersection of Sets**

*If we have two sets A and B then the intersection of both sets will be the common elements of A and B sets.*

Example:

A= {4, 6, 9, 10, 12}, B= {1, 3, 5, 7, 9, 11, 13}

A∩B= {4, 6, 9, 10, 12} ∩ {1, 3, 5, 7, 11, 13}

A∩B= {9} The intersection of B∩A will also be same as A∩B.

*The green area shows the A*∩B and B∩A

**3: Difference of Sets**

*If we have two sets A and B, and we want to find the A- B, The difference of sets will contain *all elements of set A which does not belong to *set B.*

Example:

A= {1, 2, 3, 4, 5, 6, 7, 8}, B= {1, 2, 3, 4, 5}

A-B = {1, 2, 3, 4, 5, 6, 7, 8} – {1, 2, 3, 4, 5}

A-B = {6, 7, 8}

B-A = {1, 2, 3, 4, 5} – {1, 2, 3, 4, 5, 6, 7, 8} B-A= { }

*The green area showing the A-B*.

**4: Complement of Set**

*We know, that when U be the universal set and A is a subset of U. Then the complement of A is the set of all elements of U which are not the elements of A.*

The complement of set A is denoted by A^{’}

Example:

U= {a, b, c, d, e, f, g, h,}, A= {a, b, c, d}

A^{’} = U-A

U-A= {a, b, c, d, e, f, g, h}-{a, b, c, d} U-A= {e, f, g, h}

**Frequently Asked Question-FAQs**

### What are **Set Operations** in Set Theory?

Set operations are the mathematical operations that are applied to two or more sets in order to develop a relationship between them. There are four main kinds of set operations:

### What are the Different Set Operations?

There are four main kinds of set operations: intersection, union, difference, and complement.

### Which of the Set Operations are Commutative and not Commutative?

Union and Intersection of sets are set operations that are commutative whereas the set difference is not commutative

### How do you Solve Set Operations Problems?

To solve set operation problems, we use a Venn diagram to represent the relationship between the sets and apply the set operations formula for union, intersection, difference, or complement of a set.

### What are the Set Operations Symbols?

There are different symbols used for different set operations, which are collectively referred to as set notation. For the union of sets, we use ‘∪’, for the intersection of sets, we use ‘∩’, for the difference of sets, we use ‘ – ‘, and for the complement of a set A, we write it as A’ or A^{c}.

### How do you Find the Difference Between the Two Sets?

For any two sets A and B, the difference A – B lists all the elements in set A that are not in set B.

### What are the Union and Intersection operations of Sets?

For any two sets A and B, the union is defined as the combination of elements in both set A and B. Intersection of sets gives the common elements in set A and set B.

### How do you Find the Complement of a Set?

The complement of a set A is the set of all elements in the universal set U that are not in A.

### How Do We Use Set Operations in Real Life?

A set is a collection of distinct elements. Some examples of sets in real life are a list of all the countries in the world, a list of all shapes in geometry, or a list of all whole numbers from 1 to 100. The intersection set operation lets us determine which regions are shared by two sets.

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