Venn Diagrams



-Representing a set by using a Venn Diagram
-Solving problems on sets by using Venn Diagram
-Interpreting information from Venn Diagram
Operations with sets

Operations with sets

 

-Finding union of two sets
-Finding the complement of a set
-Finding the number of elements in the union and intersection of two sets
Subsets

Subsets


-Definition of subset
-Listing subsets of a given set
-Difference between proper and improper subset
-Calculating the number of subsets in a set
Types of Sets

Types of Sets


-Define a universal set and an empty set
-Differences between finite and infinite sets
-Differences between equivalent and equal sets

Description of sets


 -Definition of sets

-Listing members of a set

-Naming a set

-Distinguishing sets by listing and stating the members

Inverse of Relations

 


The inverse of a relation R is represented by R-1

When the relations is represented using ordered pair, R-1 is obtained by reversing the order in all the ordered pairs belonging to R

Graphs of relations

 


Graphs that involve equations are drawn using all procedure used to draw the graphs of equations. For example when drawing the graphs of linear equations we can use table of values or using x and y intercepts.

The relations involving inequalities are drawn as when drawing equations, the difference is that in graphing inequalities:

  • when > or < symbol is used we draw the graph using dotted lines while when >= (greater than or equal) or <= (less than or equal symbol) is used we draw a line using bolded line.
  • we normally shade the area satisfying the given relation
  • domain and range is found by considering the values of x and y in an area where our graph covers

Domain and range of relations

 


For the given relation represented in ordered pair, all the elements of the first set are Domains while those in the second set are range. For example a relation R = {(x, y): (1, 2), (a, b), (4, 5), (9, 10)}  

Domain = {1, a, 4, 9} and range = {2, b, 5, 10}

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