Let W denote the words in the English dictionary, Define the relation R by : $\mathrm{R}=\left\{\right(\mathrm{x},\mathrm{y})\in \mathrm{W}\times \mathrm{W}\mathrm{ }$the words x and y have atleast one letter in common} Then R is

Let $\mathrm{x}\in \mathrm{W}$, then x, x have every letter common

 $\therefore (\mathrm{x},\mathrm{x})\in \mathrm{R}$

Thus R is reflexive
Let $(\mathrm{x},\mathrm{y})\in \mathrm{R},$ then x, y have atleast one letter in common
$\therefore$ y, x have atleast one letter in common thus R is symmetric
Let $\mathrm{x}=\mathrm{AND},\mathrm{y}=\mathrm{NEXT}.\mathrm{z}=\mathrm{HER}\text{ then }(\mathrm{x},\mathrm{y})\in \mathrm{R},(\mathrm{y},\mathrm{z})\in \mathrm{R}\text{ but }(\mathrm{x},\mathrm{z})\notin \mathrm{R}$ thus R is not transitive