Question

Let $W$ denotes the words in the English dictionary. If the relation $R$ is given by

$R=\left\{\right.\left(x , \, y\right)\in W\times W:the \, word \, x \, and \, y \, have \, at \, least \, one \, letter \, in \, common\left.\right\},$ then $R$ is

• A. reflexive, symmetric and not transitive
• B. reflexive, symmetric and transitive
• C. reflexive, not symmetric and transitive
• D. not reflexive, symmetric and transitive

Answer 1

Answer: (A)

Given, $R = \left\{\right. \left(\right. x , y \left.\right) \in W \times W :$ the word $x$ and $y$ have atleast one letter in common}
Let, $W=\left\{\right.cat, \, toy, \, you,\ldots \left.\right\}$
Clearly, $R$ is reflexive and symmetric but not transitive.
[Since, $cat R toy, \, toy R you\nRightarrow \, cat R you$ ]