Mathematical Relations Dr Ron Smith Graceland University Mathematical

  • Slides: 17
Download presentation
Mathematical Relations Dr. Ron Smith Graceland University

Mathematical Relations Dr. Ron Smith Graceland University

Mathematical relations n We can draw a picture to illustrate a relation between members

Mathematical relations n We can draw a picture to illustrate a relation between members of a set. Me Widow Father Daughter

Mathematical Relations n Spouse Me Widow Father Daughter

Mathematical Relations n Spouse Me Widow Father Daughter

Mathematical Relations n n This is a directed graph (digraph). Dots are vertices, arrows

Mathematical Relations n n This is a directed graph (digraph). Dots are vertices, arrows are edges. Me Widow Father Daughter

Mathematical Relations n Birth Parent Me Widow Father Daughter

Mathematical Relations n Birth Parent Me Widow Father Daughter

Mathematical relations n n A step parent is the spouse of a birth parent.

Mathematical relations n n A step parent is the spouse of a birth parent. A parent is either a birth parent or a step parent. A grandparent is a parent of a parent. We combine these simpler relations to get the complex relation “Grandparent”

Adjacency Matrices n Construct an adjacency matrix for “Spouse”. Me Father S= Widow Daughter

Adjacency Matrices n Construct an adjacency matrix for “Spouse”. Me Father S= Widow Daughter M F W D 0 0 1 1 0 0 0 0

Adjacency Matrices n “Birth Parent” Me Father B= Widow Daughter M F W D

Adjacency Matrices n “Birth Parent” Me Father B= Widow Daughter M F W D 0 0 1 0 0 0 0 0 1 0

Adjacency Matrices n n To combine “Spouse” and “Birth Parent” to get “Step Parent”

Adjacency Matrices n n To combine “Spouse” and “Birth Parent” to get “Step Parent” we simply multiply the adjacency matrices! To combine “Birth Parent” or “Step Parent” to get “Parent” we add the adjacency matrices.

A step parent is the spouse of a birth parent Spouse OF Birth Parent

A step parent is the spouse of a birth parent Spouse OF Birth Parent 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 Me Widow Father Daughter Step Parent!

A parent is a birth parent OR a step parent Birth Parent OR Step

A parent is a birth parent OR a step parent Birth Parent OR Step Parent 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 Me Widow Father Daughter Parent!

Technical Note n n n We need to use computer logic instead of arithmetic

Technical Note n n n We need to use computer logic instead of arithmetic x AND y = 1 if x and y are both 1, and 0 otherwise. We use • to stand for AND 1 • 1= 1 0 • 1= 0 1 • 0= 0 0 • 0= 0

Technical Note n n x OR y is 1 if either x or y

Technical Note n n x OR y is 1 if either x or y (or both) is 1, and 0 otherwise. We use + to stand for OR 1+1=1 0+1=1 1+0=1 0+0=0

Technical Note n n In fact, the logical operations AND and OR work exactly

Technical Note n n In fact, the logical operations AND and OR work exactly like multiplication and addition except for the fact that 1+1=1 instead of 2. If we do matrix operations using AND and OR on adjacency matrices, we get the adjacency matrix of the combined relation!

A grandparent is a parent of a parent Parent OF Parent 0 0 0

A grandparent is a parent of a parent Parent OF Parent 0 0 0 1 1 0 0 0 1 0 0 0 1 Me Widow Father Daughter Grandparent!

I’m my own Grandpa! I’m my own Grandpa, And my daughter’s her own Grandma,

I’m my own Grandpa! I’m my own Grandpa, And my daughter’s her own Grandma, It seems funny, I know, but I Mathematically show-- that I’m my own Grandpa!

The End

The End

Graceland University Life Portfolio Guiding Students to HighGraceland University Life Portfolio Guiding Students to High
MATHEMATICAL MODEL Mathematical Model Mathematical Model Mathematical ModelMATHEMATICAL MODEL Mathematical Model Mathematical Model Mathematical Model
Growing Groundwater Grievances in Graceland The Memphis SandGrowing Groundwater Grievances in Graceland The Memphis Sand
Growing Groundwater Grievances in Graceland The Memphis SandGrowing Groundwater Grievances in Graceland The Memphis Sand
Relations Chapter 9 Combining Relations Given two relationsRelations Chapter 9 Combining Relations Given two relations
INTERNATIONAL RELATIONS International Relations n International public relationsINTERNATIONAL RELATIONS International Relations n International public relations
MARKETING PUBLIC RELATIONS Public Relations marketing public relationsMARKETING PUBLIC RELATIONS Public Relations marketing public relations
UNITII Relations and Their Properties Relations Binary relationsUNITII Relations and Their Properties Relations Binary relations
Public Relations What is public relations Public relationsPublic Relations What is public relations Public relations
CHAPTER 27 Industrial Relations Industrial Relations Industrial relationsCHAPTER 27 Industrial Relations Industrial Relations Industrial relations
Unit 9 Functions and Relations Relations Functions RelationsUnit 9 Functions and Relations Relations Functions Relations
Aplikasi Media Relations Kegiatan Media Relations MEDIA RELATIONSAplikasi Media Relations Kegiatan Media Relations MEDIA RELATIONS
INDUSTRIAL RELATIONS Industrial Relations The Industrial Relations orINDUSTRIAL RELATIONS Industrial Relations The Industrial Relations or
Sense relations Lexical and sense relations Lexical relationsSense relations Lexical and sense relations Lexical relations
Public Relations Rundown Public Relations Public relations isPublic Relations Rundown Public Relations Public relations is
Relations and Function Relations and Function Relations andRelations and Function Relations and Function Relations and