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 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
Held on 30 Apr 2006 · Verified 6 Jul 2026.
not reflexive, symmetric and transitive
reflexive, symmetric and not transitive
reflexive, symmetric and transitive
reflexive, not symmetric and transitive
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