JEE Main2006MathematicsSets and RelationsActual

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

Options

Anot reflexive, symmetric and transitive
Breflexive, symmetric and not transitive
Creflexive, symmetric and transitive
Dreflexive, not symmetric and transitive

Correct answer

B. reflexive, symmetric and not transitive

Step-by-step 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 .

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