Practicing Success
Let W denote the words in the English dictionary. Defined the relation R by : R = {(x, y) ∈ w × w the words x and y have at least one letter in common}. Then R is : |
Not reflexive, symmetric and transitive Reflexive, symmetric and not transitive Reflexive, symmetric and transitive Reflexive, not symmetric and transitive |
Reflexive, symmetric and not transitive |
Clearly (x, x) ∈ R ∀ x ∈ w. So, R is reflexive Let (x, y) ∈ R, then (y, x) ∈ R as x and y have at least one letter in common. So, R is symmetric. But R is not transitive for example Let x = DELHI, y = DWARKA and z = PARK then (x, y) ∈ R and (y, x) ∈ R but (x, z) ∉ R. |