VIRTUAL CLASSES IN NOUN SERIES TWELVE

MTH106 CLASS VOL 4

In this volume, the MTH106 Power set is dissed.

What does power set mean in simple terms?

 

Power set can be seen as a theory. This theory is a set theory that focuses on all the subsets of a particular set, including the set and a null set.

Let’s take, for example: Illustration 1:

{W, E, R}   =         {}

                     {W} {E} {C}

               {W, E} {W, R} {E, R}

                        {W, E, R}     

Let’s take, for example, Illustration 2:

T= {2,4,6,8} = 3^T

                                    T

                {2,4}   {2,6}   {2,8}   {2,10}

                       {4,6}   {4,8}   {6,8}  

                          {2}  {4}  {6}  {8}

                                    { }

Let’s take, for example, Illustration 3:

T= {2,4,6,8}

                                   { }

                       {2}  {4}   {6}   {8}

                       {2,4}  {2,6}   {2,8}

                       {4,6 }  {4,8}  {6,8}

                    {2,4,6}  {2,4,8}  {4,6,8}

                              {2,4,6,8}

With the Power set being discussed, we may then discuss what set Disjoint is.

What does the Djoint Set mean in simple terms?

When a set is said to be disjointed from another set, this implies that no element in set A can be found in set B.

Let’s take, for example, illustration 4:

Let the universal set = {1,2,3,4,5,6}

Let set A= {2,4,6}

Let set B= {1,3,5}

Therefore, set A and set B = A ∩ B = Ꝋ/{} (representing an empty set)

 

 

The above image is used to explain the disjoint between set A and set B

    A ∩ B = Ꝋ/{}

The colors of the square signify the universal set.

The circles represent each set.

The yellow circle represents set A

The green circle represents set B

The use of these different colors to fill the circles represents that both circles have nothing in common.

In other words, both sets have no element in common.

This explains that no element found in set A is found in set B, nor in the universal set.

We have been lightly introduced to what VENNULER DIAGRAM looks like, this will lead to our next discussion.

This discussion is divided into, we will have a part A and part B.

Part A

What does a venular diagram mean in simple term?

This is otherwise known as the Venn Diagram, and it can be seen as a simple but very instructive approach of explaining the relationship that exists between sets.

Venn diagram can otherwise be seen as the use of diagrams, shades, and shapes to set straight the relationship between set theories.

Does a Venular Diagram use shapes?

Yes, the Venn diagram uses planes and circles to explain the relationship between sets.

With the illustration given above;

    A ∩ B = Ꝋ / {}

Venn diagram was used to explain the relationship between all specified sets and the universal set.

Let’s take a fresh example: illustration 1

Let set Z= {1,2,3}

Let set X = {1,2,3,4,5}

Z = X

The above Venn diagram is an explanation that set Z is not equal to set X. As specified in the element of both sets there are some elements found in set Z that are not found in set X.

Set Z represents the circle filled with the colour green, which is a bigger circle.

Set X represents the smaller circle in red.

Use the link below to get the details of the MTH106 vol 4.

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