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Let W denote the words in the English dictionary. Define the relation R by :
$R=\{(x, y) \in W \times W \mid$ the words $x$ and $y$ have at least one letter in common $\}$. Then $R$ is
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$R=\{(x, y) \in W \times W \mid$ the words $x$ and $y$ have at least one letter in common $\}$. Then $R$ is
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reflexive, symmetric and not transitive
reflexive, symmetric and not transitive
Clearly $(\mathrm{x}, \mathrm{x}) \in \mathrm{R} \forall \mathrm{x} \in \mathrm{W}$. So, $\mathrm{R}$ is reflexive.
Let $(x, y) \in R$, then $(y, x) \in R$ as $x$ and $y$ have at least one letter in common. So, $R$ is symmetric.
But $R$ is not transitive for example
Let $x=$ DELHI, $y=$ DWARKA and $z=$ PARK
then $(x, y) \in R$ and $(y, z) \in R$ but $(x, z) \notin R$.
Let $(x, y) \in R$, then $(y, x) \in R$ as $x$ and $y$ have at least one letter in common. So, $R$ is symmetric.
But $R$ is not transitive for example
Let $x=$ DELHI, $y=$ DWARKA and $z=$ PARK
then $(x, y) \in R$ and $(y, z) \in R$ but $(x, z) \notin R$.
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