Discrete Math

Define the sets$X=\{1,2,3\}$ and $Y=\{4,5,6\}$ . Now, define the relation R from X to Y by $}_{\left\{x\right\}}{R}_{y$ if and only if $x-y$ is even. Find all of the elements in R.

Define the sets

glasskerfu
2021-08-14
Answered

Discrete Math

Define the sets$X=\{1,2,3\}$ and $Y=\{4,5,6\}$ . Now, define the relation R from X to Y by $}_{\left\{x\right\}}{R}_{y$ if and only if $x-y$ is even. Find all of the elements in R.

Define the sets

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casincal

Answered 2021-08-15
Author has **82** answers

Step 1

Let$x=\{1,2,3\}$

and$4=\{4,5,6\}$

and$R\subseteq X\times Y$

Such that$}_{x}{R}_{y$ if f $x-y$ is even.

Step 2

$X\times Y=\{(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)\}$

$R=\{(x,y)\in X\times Y\mid X-Y\text{is even}\}$

$=\{(1,5),(2,4),(2,6),(3,5)\}$

Let

and

and

Such that

Step 2

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can I say that the Relation R is Reflexive and also a Symmetric because I have (a,b) and (b,a) and also (a,a).

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