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Check whether the relation $R$ defined in the set $\{1,2,3,4,5,6\}$ as
$R=\{(a, b): b=a+1\}$ is reflexive, symmetric or transitive.
$R=\{(a, b): b=a+1\}$ is reflexive, symmetric or transitive.
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(i) $\mathrm{R}$ is not reflexive $a \neq a+1$.
(ii) $\mathrm{R}$ is not symmetric if $\mathrm{b}=\mathrm{a}+1$, then $\mathrm{a} \neq \mathrm{b}+1$
(iii) $\mathrm{R}$ is not transitive if $\mathrm{b}=\mathrm{a}+1, \mathrm{c}=\mathrm{b}+1$ then $\mathrm{c} \neq \mathrm{a}+1$.
(ii) $\mathrm{R}$ is not symmetric if $\mathrm{b}=\mathrm{a}+1$, then $\mathrm{a} \neq \mathrm{b}+1$
(iii) $\mathrm{R}$ is not transitive if $\mathrm{b}=\mathrm{a}+1, \mathrm{c}=\mathrm{b}+1$ then $\mathrm{c} \neq \mathrm{a}+1$.
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