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Show that the relation \( R \) in the set \( \mathbf{R} \) of real numbers, defined as \( R= \) \( \left\{(a, b): a \leq b^{2}\right\} \) is neither reflexive nor symmetric nor transitive.
Check whether the relation \( \mathrm{R} \) defined in the set \( \{1,2,3,4,5,6\} \) as \( \mathrm{R}=\{(a, b): b=a+ \) 1 ) is reflexive, symmetric or transitive.
Show that the relation \( \mathrm{R} \) in \( \mathbf{R} \) defined as \( \mathbf{R}=\{(a, b): a \leq b\} \), is reflexive and - transitive but not svmmetric.
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