Sets, Relations and Function: Let W denote the words in the English dictionary. Define the… | AIEEE 2006

AIEEE 2006 (Offline)Question 1

Let $W$ denote the words in the English dictionary. Define the relation $R$ by $R=\{(x,y)\in W\times W\mid\text{the words }x\text{ and }y\text{ have at least one letter in common}\}$. Then, $R$ is

Sets, Relations and Function

reflexive, symmetric and not transitive✓ Correct answerreflexive, symmetric and transitivereflexive, not symmetric and transitivenot reflexive, symmetric and transitive

Solution

Every word shares a letter with itself and the relation is clearly symmetric, but e.g. INK–KING share K, KING–GO share G, while INK and GO share none, so $R$ is not transitive.

Sets, Relations and Function - JEE Mathematics question (AIEEE 2006 (Offline))

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