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Questions  

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 atleast one letter in common} Then R is

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By Expert Faculty of Sri Chaitanya
a
reflexive, symmetric and not transitive
b
reflexive, symmetric and transitive
c
reflexive, not symmetric and transitive
d
not reflexive, symmetric and transitive
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detailed solution

Correct option is A

Let xW, then x, x have every letter common

 (x,x)R

Thus R is reflexive
Let (x,y)R, then x, y have atleast one letter in common
 y, x have atleast one letter in common thus R is symmetric
Let x=AND,y=NEXT.z=HER then (x,y)R,(y,z)R but (x,z)R thus R is not transitive


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