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Question

Let W denotes the words in the English dictionary Define the relation R by R={(x,y)W×W} the ward x and y have at least one letter in common. Then R is


A

Not reflexive, symmetric, and transitive

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B

Reflexive, symmetric, and not transitive

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C

Reflexive, symmetric, and transitive

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D

Reflexive, not symmetric, and transitive

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Solution

The correct option is B

Reflexive, symmetric, and not transitive


Explanation for the correct answer:

The given relation is R={(x,y)W×W} the words x and y have at least one letter in common

Checking for Reflexive Property:

(a,a)R

IfaW,a=RAM (say)

R is reflexive

Checking for Symmetric Property:

(RAM,AAM)R

(AAM,RAM)R

If (a1,a2)R and (a2,a1)R, then R is symmetric.

Checking for Transitive Property:

If (a1,a2)R and (a2,a3)R, then (a1,a3)R

a1=RAM,(a1,a2)Ra2=NAAM,(a2,a3)Ra3=NONE,(a1,a3)R

R is not transitive.

Hence, the correct option is (B)


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