Let W denote the words in the English Dictionary. Define the relation R by R = (x, y) ∈ W × W: the words x and y have at least one letter common then R is

Question

Let W denote the words in the English Dictionary. Define the relation R by R = (x, y) ∈ W × W: the words x and y have at least one letter common then R is (A) reflexive, not symmetric and transitive (B) not reflexive, symmetric and transitive (C) reflexive, symmetric and not transitive (D) reflexive, symmetric and transitive

Tardigrade Admin · Accepted Answer

(x, x) ∈ R ∀ x ∈ W as all letters in both are common. If (x, y) ∈ R then x and y have a letter in com operatornamemon ⇒(y, x) ∈ R. Next, let x= fix, y= operatornamesix and z= operatornameson then (x, y) ∈ R, (y, z) ∈ R but (x, z) ∉ R So R is reflexive, symmetric but not transitive

Q. Let W denote the words in the English Dictionary. Define the relation R by R={(x,y)∈W×W : the words x and y have at least one letter common \}, then R is

reflexive, not symmetric and transitive

not reflexive, symmetric and transitive

reflexive, symmetric and not transitive

reflexive, symmetric and transitive

(x,x)∈R∀x∈W as all letters in both are common. If (x,y)∈R then x and y have a letter in common⇒(y,x)∈R. Next, let x= fix, y=six and z=son then (x,y)∈R, (y,z)∈R but (x,z)∈/R So R is reflexive, symmetric but not transitive

Q. 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 common \}, then $R$ is