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

1. Reflexive: Every word $x$ has all its letters in common with itself. So $(x,x)\in R$. It is reflexive.2. Symmetric: If $x$ and $y$ have a common letter, then $y$ and $x$ also have that same common letter. So $(x,y)\in R⟹(y,x)\in R$. It is symmetric.3. Transitive: Let $x=\text{DELHI}$, $y=\text{DWARKA}$, $z=\text{PARK}$.$x$ and $y$ have 'D' in common $⟹(x,y)\in R$.$y$ and $z$ have 'A', 'R', 'K' in common $⟹(y,z)\in R$.However, $x$ (DELHI) and $z$ (PARK) have no letters in common $⟹(x,z)\notin R$.It is not transitive.