Let W denotes the words in the English dictionary. If the relation R is given by R= .(x , y)∈ W× W:the word x and y have at least one letter in common. then R is

Question

Let W denotes the words in the English dictionary. If the relation R is given by R= .(x , y)∈ W× W:the word x and y have at least one letter in common. 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

Tardigrade Admin · Accepted Answer

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

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

$R = {(x, y) \in W \times W : t h e w or d x an d y ha v e a t l e a s t o n e l e tt er in co mm o n},$ then $R$ is

reflexive, symmetric and not transitive

reflexive, symmetric and transitive

reflexive, not symmetric and transitive

not reflexive, symmetric and transitive

Given, $R = {(x, y) \in W \times W :$ the word $x$ and $y$ have atleast one letter in common}
Let, $W = {c a t, t oy, yo u, \dots}$
Clearly, $R$ is reflexive and symmetric but not transitive.
[Since, $c a tRt oy, t oy R yo u ⇏ c a tR yo u$ ]

Q. Let W denotes the words in the English dictionary. If the relation R is given by R={(x,y)∈W×W:thewordxandyhaveatleastoneletterincommon}, then R is