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Let $R$ be the relation in the set $\{1,2,3,4\}$ given by $R=\{(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)\}$. Choose the correct answer.
(a) $\mathrm{R}$ is reflexive and symmetric but not transitive.
(b) $R$ is reflexive and transitive but not symmetric.
(c) $\mathrm{R}$ is symmetric and transitive but not reflexive.
(d) $\mathrm{R}$ is an equivalence relation.
(a) $\mathrm{R}$ is reflexive and symmetric but not transitive.
(b) $R$ is reflexive and transitive but not symmetric.
(c) $\mathrm{R}$ is symmetric and transitive but not reflexive.
(d) $\mathrm{R}$ is an equivalence relation.
Solution:
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(b)
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