let R be the relation in the set n given by R={(a,b)|a>b} Show that the relation neither reflexive nor symmetric but transive

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$$\begin{gathered} \mathrm{R}=\left\{\left(\mathrm{a},\mathrm{b}\right)| \mathrm{a}>\mathrm{b}\right\} \\ \mathrm{As} \mathrm{a}>\mathrm{a} \mathrm{is} \mathrm{not} \mathrm{possible}, \mathrm{hence} \\ \mathrm{R}=\left\{\left(\mathrm{a},\mathrm{a}\right)| \mathrm{a}>\mathrm{a}\right\} \mathrm{is} \mathrm{false}, \mathrm{hence} \mathrm{relation} \mathrm{is} \mathrm{not} \mathrm{reflexive}. \\ \mathrm{If} \mathrm{a}>\mathrm{b} \mathrm{is} \mathrm{true}, \mathrm{then} \mathrm{b}>\mathrm{a} \mathrm{cannot} \mathrm{be} \mathrm{true}. \mathrm{Hence} \\ \mathrm{R}=\left\{\left(\mathrm{b},\mathrm{a}\right)| \mathrm{b}>\mathrm{a}\right\}, \mathrm{hence} \mathrm{relation} \mathrm{is} \mathrm{not} \mathrm{symmetric}. \\ \mathrm{Now} \mathrm{if} \\ \mathrm{a}>\mathrm{b} \mathrm{and} \mathrm{b}>\mathrm{c} \mathrm{are} \mathrm{true}, \mathrm{then} \\ \mathrm{a}>\mathrm{c} \mathrm{will} \mathrm{always} \mathrm{be} \mathrm{true}. \\ \mathrm{Hence} \\ \mathrm{R}=\left\{\left(\mathrm{a},\mathrm{b}\right)| \mathrm{a}>\mathrm{b}\right\} \mathrm{and} \mathrm{R}=\left\{\left(\mathrm{b},\mathrm{c}\right)| \mathrm{b}>\mathrm{c}\right\} \mathrm{then} \\ \mathrm{R}=\left\{\left(\mathrm{a},\mathrm{c}\right)| \mathrm{a}>\mathrm{c}\right\} \mathrm{will} \mathrm{always} \mathrm{be} \mathrm{true}. \\ \mathrm{Hence} \mathrm{relation} \mathrm{is} \mathrm{transitive}. \end{gathered}$$

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