Types of Sets || Sets Part 3

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Sets Representation(https://vaishalianandtutorials.blogspot.com/2020/05/sets-representation-roster-and-set.html)

Today's topic is:-

Types of Sets

There are mainly 10 types:-

1. Empty Set
2. Singleton Set
3. Equal Set
4. Proper Subset
5.Improper Subset
6. Subset
7. Power Set
8. Universal Set
9.Finite Set
10. Infinite Set

Let's look at them one by one....

Empty Set

• An empty/null set is a set with no elements.
• It is denoted by phi(Φ). 
• Eg. A set of natural no. less than 1 i.e. Φ.

Singleton Set

• Singleton sets are the sets with only one element.
• Example: A set of natural no. less than 2 i.e. {1}.
  

Finite Set

• Finite sets are sets with finite no. of elements.
• Example: A set of natural no. less than 10 i.e. {1,2,3,4,5,6,7,8,9}

Infinite Set

• Infinite sets are sets with infinite no. of elements.
• Example: set of natural no. more than one i.e.{1,2,3,4,............}

Equal Set

• Equal sets are 2 sets with exactly same elements.
• For Example: A set of natural no. less than 4 and a set of whole no. between 0 and 4 both are equal to {1,2,3}.

Universal Set

• A universal set is the set containing all objects or elements and of which all other sets are subsets.
• It is denoted by U.
• For Example: The set of all alphabets is the universal set for set of vowels and set of constants.

Subset

• A subset B of a set A is the set of elements that are present in A.
• Example: The set of vowels is the subset of all alphabets.
• Also A is called the Superset of B.

Power Set

• Power Set is the set of all subsets of a set.
  
• Example: A= {1, 2}
• P(A)={Φ,{1},{2},{1,2}}

Proper Subset

• A proper subset contains some but not all elements of an original set.
• It is denoted by A⊂B
• Example: A= {1,2,3} and B ={1,2,3,4,5}

Improper Subset

• It is a set containing every element of the original set
• It is denoted by A⊆B
• Example: A ={1,2,3} and B = {1,3,2}

Practice

Q1. Which of the following sets is a universal set for the other four sets?

(a) The set of even natural numbers
(b) The set of odd natural numbers
(c) The set of natural numbers
(d) The set of negative numbers
(e) The set of integers

Ans. As we know that integers contain both positive and negative numbers. Also it contains all natural numbers. So, the correct answer is e.

Q2. Classify the following as finite and infinite sets.

(a) The set of days in a week
 => As we know that there are only 7 days in a week .Therefore, Finite.

(b) A = {x : x ∈ N  x > 1}
 => As we know there are infinite i.e. never ending natural numbers greater than one existing so  Infinite

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