The relation $R=\{(x, y): x, y \in \mathbb{Z}$ and $x+y$ is even $\}$ is:
Solution
<p>$R=\{(x, y): x, y \in z$ and $x+y$ is even $\}$</p>
<p>reflexive $x+x=2 x$ even</p>
<p>symmetric of $x+y$ is even, then $(y+x)$ is also even</p>
<p>transitive of $\mathrm{x}+\mathrm{y}$ is even $\& \mathrm{y}+\mathrm{z}$ is even then $x+z$ is also even</p>
<p>So, relation is an equivalence relation.</p>
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
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