Let $R$ be a relation on $Z \times Z$ defined by $(a, b) R(c, d)$ if and only if $a d-b c$ is divisible by 5. Then $R$ is
Solution
<p>$(a, b) R(a, b)$ as $a b-a b=0$</p>
<p>Therefore reflexive</p>
<p>Let $(a, b) R(c, d) \Rightarrow a d-b c$ is divisible by 5</p>
<p>$\Rightarrow \mathrm{bc}-\mathrm{ad}$ is divisible by $5 \Rightarrow(\mathrm{c}, \mathrm{d}) \mathrm{R}(\mathrm{a}, \mathrm{b})$</p>
<p>Therefore symmetric</p>
<p>Relation not transitive as $(3,1) \mathrm{R}(10,5)$ and $(10,5) \mathrm{R}(1,1)$ but $(3,1)$ is not related to $(1,1)$</p>
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
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