Set, Relation and FunctionEasy
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 in common}. Then R is
R = {(x, y) ∈ W × W | the words x and y have at least one letter in common}. Then R is
Options
A.not reflexive, symmetric and transitive
B.reflexive, symmetric and not transitive
C.reflexive, symmetric and transitive
D.reflexive, not symmetric and transitive
Solution
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, z) ∈ R but (x, z) ∉ R
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, z) ∈ R but (x, z) ∉ R
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