Discrete Mathematics Relation

Introduction to discrete mathematics relation:

The discrete mathematics deals with functions and their properties, we noted the important property that all functions must have, namely that if a function does map a value from its domain to its co-domain, it must map this value to only one value in the co-domain.

Writing in set notation, if a is some fixed value:

` |{f(x)|x=a}|=1`

However, when we consider the relation, we relax this constriction, and so a relation may map one value to more than one other value. Having problem with Systems of Equations Solver keep reading my upcoming posts, i will try to help you.


Properties of discrete mathematics relation:-


In the following properties of discrete mathematics relation:-

Reflexive
Symmetric
Transitive
Antisymmetric
Trichotomy
Reflexive

Relation of the equality, = is reflexive. Examine that for all numbers a = a.So "=" is reflexive.

Symmetric

Relation is symmetric the values a and b:  a R b implies b R a.These type of relation is symmetric.

Transitive

Relation is transitive of all values of a, b, c: a R b and b R c implies a R c.These type of relation is transitive.

Antisymmetric

A relation is antisymmetric for all values a and b: a R b and b R a implies that a=b.These type of relation is antisymmetric

Trichotomy

A relation satisfy the all values a and b it holds true that: xRy or yRx.The  two relation numbers a and b, it is true that whether a ≥ b or b ≥ a (both if a = b).These type of relation is trichotomy. Please express your views of this topic How to Find Volume of a Cone by commenting on blog.


Example problems for discrete mathematics relation:-


Problem 1:-

`Let A = {1, 2, 3, 4, 5} and R : A harrA :-= {(a, b) : a |b}. What barR and R^-1?`

Solution:-

`{(1, 1) , (1, 2) , (1, 3) , (1, 4) , (1, 5) , (2, 2) , (2, 4) , (3, 3) , (4, 4) , (5, 5)}`

`barR = {(2, 1) , (2, 3) , (2, 5) , (3, 1) , (3, 2) , (3, 4) , (3, 5) , (4, 1) , (4, 2) , (4, 3) , (4, 5) , (5, 1) , (5, 2) , (5, 3) , (5, 4)}`

`R^-1 = {(1, 1) , (2, 1) , (3, 1) , (4, 1) , (5, 1) , (2, 2) , (4, 2) , (3, 3) , (4, 4) , (5, 5)}`

Problem 2:-

For each of the following relations of  pair which satisfies the relation ,and another pair which doesn't say whether each relation is reflexive relation,symmetric relation,transitive relation or anti-symmetric relation form discrete mathematics
(a) The relation on {1,2,3,4,5} defined by {(a,b)| a-b is even}
(b) The relation on {1,2,3,4,5} defined by {(a,b)| a+b is even}
(c) The relation on P, the set of all people,defined by {(a,b) | a and b have a common ancestor}

Solution:-

(a) The pair (4,2) satisfies the relation,(2,1) doesn't includes other relation.
(b) (3,3) satifies the relation,(3,2) doesn't includes other relation.
(c) (Bart,Lisa) satisfies the relation,(Homer,Marge) doesn't includes other relation.