Question

Let A= {1, 2, 3, 4, 5}then define a relation R on A as (a.b)∈R iff a≤b and Relation Ton A as (a,b)∈T iff a/b.

Represent R by a matrix.
Is R Reflexive? Transitive? Give a valid reason for your answer.
Is T Antisymmetric? Give a valid reason for your answer.
Represent T by an matrix
Represent T by an arrow diagram.

Answer 1

A={1,2,3,4,5}

RELATION shows in matrix form

Relation = $\begin{bmatrix} 1& 1 & 1 & 1 & 1 \\ 0 & 1 & 1 & 1 & 1\\ 0 & 0& 1& 1 &1\\ 0 & 0& 0 & 1&1\\ 0&0&0&0&1\\ \end{bmatrix} ​ ​ ​ ​ ​ ​$

Reflexive:all diagonal elements be 1

Transitivity: aRb and bRc then aRc

Matrix shows transitivity

Relation ton=

$\begin{bmatrix} 1& 1& 1&1&1\\ 0&1&0&1&0\\ 0&0&1&0&0\\ 0&0&0&1&0\\ 0&0&0&0&1\\ \end{bmatrix}$

Matrix shows reflexive all diagonal elements be 1

Antisymmetric shows : i Relate to j then j not relate to y