Sets - Sets

Sets are described as a set of well-defined items or components which are invariable. A set shall be represented by a capital letter. The number of elements in the finite collection is referred to as the cardinal number of the set. 

We've got a few forms of sets in Mathematics. They are void sets, finite and infinite sets, proper sets, equivalent sets, etc. 

Empty set  

A set that does not contain any product is called an empty or a null set. It is implied by {} or Ø. 

Set of singleton 

A set comprising a single element is considered a singleton set. 

Finite set  

A set composed of a certain number of elements is considered a finite set. 

Infinite Set 

A set that is not finite is considered an infinite set. 

Set of Equivalent 

If the number of elements is the same for two distinct sets, they are considered identical sets. The order of the sets doesn't apply here. It shall be expressed as:   

n(a) = n (B) h 

Where A and B are two sets with the same number of components. 

Equal set 

The two sets A and B are considered identical if they contain precisely the same elements; the elements’ order does not matter. 

Disjoint Sets 

The two sets A and B are said to be disjointed if there is no common element in the set. 

Subsets 

Set 'A' can be called a subset of B if each element of A is an element of B as well. Even the null collection is known to be a subclass of a different set. In general, a subset is part of a different set. 

Proper subset 

If A is true for B and A is valid for B, so A is considered the proper subset for B and may be written as A is valid for B. 

Superset 

If set A is a subset of set B, and all the set B elements are set A, set A is a superset of set B. A-B denotes it. 

Universal Set 

A set comprising all sets related to a certain situation is considered a universal set. It's the set of all potential values.

Importance and Weightage

This concept is taught under the chapter Sets. You will learn about the different types of sets and use them to solve complex questions. The weightage of this topic is 11 marks in your final exam.

1. Find C U D and C ⋂ D and C – D.

If C = {a, b, c, d} and D = {c, d}.

Solution: 

C = {a, b, c, d} and D = {c, d}

C U D  = {a, b, c, d} 

C ⋂ DD = {c, d} and 

C – D = {a, b}

2. Write the set {1, 4, 9, 16, 25, . . . } in builder form.

Solution: 

A = {x : x is the square of a natural number}

A = {x : x = n2 , where n ∈ N}

3. What are the subsets of {1,2,3}?

Solution: φ, {1},{2},{3},{1,2},{2,3},{1,3},{1,2,3}

Q: What is a set?

Q: What are the different types of sets?

Q: Why do we use sets of maths?

Q: What are the set elements?

Q: What are the different types of sets?