Let W denote the words in the English dictionary. Define the relation R by : $R=\{(x, y) \in W imes W \mid$ the words $x$ and $y$ have at least one letter in common $\}$. Then $R$ is

Question

Let W denote the words in the English dictionary. Define the relation R by : $R=\{(x, y) \in W 	imes W \mid$ the words $x$ and $y$ have at least one letter in common $\}$. Then $R$ is

Aicharya · Accepted Answer

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 $(x, z) 
otin R$.

Let W denote the words in the English dictionary. Define the relation R by : $R=\{(x, y) \in W \times W…

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