# Discrete Math Define the sets X=\{1,2,3\} and Y=\{4,5,6\}. Now, define the

Discrete Math
Define the sets $X=\left\{1,2,3\right\}$ and $Y=\left\{4,5,6\right\}$. 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.
You can still ask an expert for help

## Want to know more about Discrete math?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

casincal
Step 1
Let $x=\left\{1,2,3\right\}$
and $4=\left\{4,5,6\right\}$
and $R\subseteq X×Y$
Such that ${}_{x}{R}_{y}$ if f $x-y$ is even.
Step 2
$X×Y=\left\{\left(1,4\right),\left(1,5\right),\left(1,6\right),\left(2,4\right),\left(2,5\right),\left(2,6\right),\left(3,4\right),\left(3,5\right),\left(3,6\right)\right\}$
$R=\left\{\left(x,y\right)\in X×Y\mid X-Y\text{is even}\right\}$
$=\left\{\left(1,5\right),\left(2,4\right),\left(2,6\right),\left(3,5\right)\right\}$