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Q.

Let W denote the words in the English dictionary. Define the relation R by :  R=x,yW×W the words x and y have atleast one letter in common} then R is

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a

Not reflexive, symmetric, Transitive 

b

Reflexive, symmetric and not transitive

c

Reflexive, symmetric, Transitive

d

Reflexive, not symmetric, transitive

answer is B.

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Detailed Solution

x,xR  xW   R is reflexive 

 x,yR then  y,xR.

R is symmetric But R is not transitive 

If x=DELHI, Y = DWARAKA, Z = PARK

x,yR,y,zR  But  z,xR

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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