Solution to Given the following set: 1. X = {1, 2, 3, 4, 5} defined by the … - Sikademy
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Archangel Macsika

Given the following set: 1. X = {1, 2, 3, 4, 5} defined by the rule (x, y) ∈ R if x + y ≤ 6 a. List the elements of R b. Find the domain of R c. Find the range of R d. Draw the digraph e. Properties of the Relation

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Let's list the elements of R:

R = \{ (1,1),\,(1,2),\,(1,3),\,(1,4),\,(1,5),\,(2,1),\,(2,2),\,(2,3),\,(2,4),\,(3,1),\,(3,2),\,(3,3),\,(4,1),\,(4,2),\,(5,1)\}

Find the domain  of the relation:

D(R) = \{ x|(x,y) \in R\} = \{ 1,2,3,4,5\} = X

Find the range  of the relation:

E(R) = \{ y|(x,y) \in R\} = \{ 1,2,3,4,5\} = X

Draw the digraph:

Find properties of the Relation:

(5,5) \notin R so R is not reflexive

(1,1) \in R so R is not irreflexive

If x + y \le 6 then y+x \le 6 so \left( {x,y} \right) \in R \Leftrightarrow \left( {y,x} \right) \in R - R is symmetric relation.

(5,1) \in R,\,(1,4) \in R , but (5,4) \notin R so R is not transitive relation.

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Question ID: mtid-5-stid-8-sqid-3312-qpid-2011