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

Let $x\in W$. Then x, x have every letter common

$\therefore (x,x)\in R$.

Thus R is reflexive.

Let $(x,y)\in R$.

Then x, y have atleast one letter in common then y , x have atleast one common 

So , R is symmetric

Let $(x,y) , \left(y,z\right)\in R$then x and y have atleast one letter common and y , z need not have common letter  

$\Rightarrow \left(x,z\right)\notin R$ 

So , R is not transitive