Contents

Part 1.....................................................................................................................................................7

With reference to the scenario, prepare a report which examines the set theory and functions

applicable to software engineering and analyze mathematical structures of objects using graph

theory....................................................................................................................................................7

Section 1................................................................................................................................................7

Perform algebraic set operations in a formulated mathematical problem...................................7

Determine the cardinality of a given bag (multi set).....................................................................7

Determine the inverse of a function using appropriate mathematical techniques.......................7

Formulate corresponding proof principles to prove properties about defined sets.....................7

Section 2................................................................................................................................................7

Model contextualized problems using trees, both quantitatively and qualitatively.....................7

Use Dijkstra's algorithm to find a shortest path spanning tree in a graph..................................7

Assess whether an Euler Ian and Hamiltonian circuit exists in an undirected graph.................7

Construct a proof of the Five Color Theorem..............................................................................7

Introduction.......................................................................................................................................8

Set Theory Definitions........................................................................................................................8

Sets Containing Numerical Data.......................................................................................................10

Set operation:...................................................................................................................................11

Union....................................................................................................................................11

Intersection:.........................................................................................................................11

Disjoint:................................................................................................................................12

Set Difference:......................................................................................................................12

Complement:........................................................................................................................12

Type of public Policy.........................................................................................................................13

Health Problem....................................................................................................................13

Road Traffic Safety education and training problem.........................................................13

Transport Problem..............................................................................................................13

Issue of Health public problem...................................................................................................13

scenario:.......................................................................................................................................13

scenario:.......................................................................................................................................15

Transport Problem......................................................................................................................17

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With reference to the scenario, prepare a report which examines the set theory and functions

 Prepare a presentation for twenty minutes that explains an application of group theory

discreate mathmatic for programming, Assignments of Mathematics

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Contents

Part 1

With reference to the scenario, prepare a report which examines the set theory and

functions applicable to software engineering and analyze mathematical structures of

objects using graph theory.

Section 1

 Perform algebraic set operations in a formulated mathematical problem.

 Determine the cardinality of a given bag (multi set).

 Determine the inverse of a function using appropriate mathematical techniques.

 Formulate corresponding proof principles to prove properties about defined sets.

Section 2

 Model contextualized problems using trees, both quantitatively and qualitatively.

 Use Dijkstra's algorithm to find a shortest path spanning tree in a graph.

 Assess whether an Euler Ian and Hamiltonian circuit exists in an undirected graph.

 Construct a proof of the Five Color Theorem.

Introduction

In this task, first I am going to introduces which set and its operation through three policy

which is based on scenario then I will find out it’s cardinality for merit. I will find inverse of

function based on scenario. After that I will describe model consolidated problem using set and

describe it quantitatively and qualitatively. Also, I use Dijkstra Algorithm to find out the

shortest path using spanning tree. At the end of task, I will be proved set law through policy

and five color theorems.

Set Theory Definitions

Emma and her sister Michelle both want to open pie shops. Emma wants to serve five kinds of

pie: chocolate, key lime, strawberry, cherry, and peach. Michelle wants to serve five kinds of pie

as well, but not exactly the same ones that Emma plans to sell. She is going to sell strawberry,

peach, apple, pear, and lemon pies.

Each of these groups of pies can be considered to be a set. In set theory, a set is collection of

objects, and each item in the set is called an element.

In this case, there are two sets. Let's call them E and M (for Emma and Michelle). Each set

contains exactly five elements. Even though most sets do contain at least one element, there are

special cases when a set contains NO elements. A set containing exactly zero elements is called

an empty set.

We can further define certain elements within a set to be in a subset, which is a smaller set of

elements taken from within a set. For example, the subset of Set E that only contains fruit pies

would contain four elements: key lime, strawberry, cherry, and peach. Chocolate would not be in

the subset even though it is an element of the larger set. (Study.com, 2019)

The complement to a set contains all the elements that are NOT in the set. For example, the

complement to set M would contain every kind of pie except for those already in the set.

Finally, disjointed sets are sets that do not have any elements in common. The intersection of two

disjointed sets would be an empty set.

Sets Containing Numerical Data

The elements of a set can numerical or non-numerical, like the pies in the previous example. Can

you think of some examples of set containing numerical data?

Let's say that set A contains all odd numbers less than or equal to 25. This means that set A

would contain the elements 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, and 25. We could also define

another set, set B, that contains all prime numbers less than or equal to 25. Set B would contain

the elements 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Which elements would be in a set formed from the intersection of set A and set B? Remember

that the intersection of two sets contains elements that are common to both sets. In this case, the

intersection would contain the elements 3, 5, 7, 11, 13, 17, 19, and 23. The elements 2, 9, 15, and

25 would NOT be in this new set because they are not found in set A and B.

Set operation: here I mention the different types of set operation which is given below.

(GeeksforGeeks, 2019)

 Union : Union of the sets A and B, denoted by A ∪ B, is the set of distinct element

belongs to set A or set B, or both.

Above is the Venn Diagram of A U B.

Example : Find the union of A = {2, 3, 4} and B = {3, 4, 5};

Solution : A ∪ B = {2, 3, 4, 5}.

 Intersection: The intersection of the sets A and B, denoted by A ∩ B, is the set of

elements belongs to both A and B i.e. set of the common element in A and B.

Above is the Venn Diagram of A ∩ B.

Example: Consider the previous sets A and B. Find out A ∩ B.

Solution : A ∩ B = {3, 4}.

Above is the Venn Diagram of Ac

Type of public Policy

 Health Problem

 Road Traffic Safety education and training problem

 Transport Problem

Issue of Health public problem

Health policy refers to decisions, plans and actions which were undertaken to achieve specific

health care goals within society. An explicit health policy could achieve several things that

include defining a vision for the future which in turn helps to establish targets and points of

reference for short and medium term.

There are many categories of health policies, including personal healthcare policy,

pharmaceutical policy and policies related to public health such as vaccination policy, tobacco