Check whether the relation \(R\) defined in the set \(\{1,2,3,4,5,6\}\) as \(\mathbf{R}=\{(a, b): b=a+1\}\) is reflexive, symmetric or transitive.
Expert Answer
\(\mathrm{R}=\{(\mathrm{a}, \mathrm{b}): \mathrm{b}=\mathrm{a}+1\}\) in the set \(\{1,2,3,4,5,6\}\).
\(\therefore \mathrm{R}=\{(1,2),(2,3),(3,4),(4,5),(5,6)\}\).
(i) \(\because(1,1) \notin \mathrm{R} \Rightarrow \mathrm{R}\) is not reflexive.
(ii) \(\because(1,2) \in \mathrm{R}\) but \((2,1) \notin \mathrm{R} . \Rightarrow \mathrm{R}\) is not symmetric.
(iii) \(\because(1,2),(2,3) \in \mathrm{R}\), but \((1,3) \notin \mathrm{R} . \Rightarrow \mathrm{R}\) is not transitive.
Verified Answer
Rated 5 out of 5
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