Solution to RELATION. Given the following set: 1. X = {1, 2, 3, 4, 5} defined by … - Sikademy
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RELATION. 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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Given the X = \{1, 2, 3, 4, 5\} define the relation R by the rule (x, y) \in R if x + y \le 6  

a. Let us find the list the elements of R:

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

b. Let us find the domain of R:

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

c. Let us find the range of R:

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

d. Let us draw the digraph of R:

e. Let us study some properties of the relation R:

Since (4,4)\notin R, the relation R is not reflexive.

If (x, y) \in R, then x + y \le 6, and hence y + x \le 6. It follows that (y, x) \in R, and the relation is symmetric.

Taking into account that (5,1)\in R and (1,5)\in R, but (5,5)\notin R, we conclude that R is not a transitive relation.

It follows that R is not an equivalence relation.  

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Question ID: mtid-5-stid-8-sqid-3307-qpid-2006