1.

LetS bethe setof allpointsin aplaneand letR bea relationin SdefinedbyR={(a,b):d(A,B)lt 2 units} whered(A,B)is thedistancebetweenthepointsA and B. ShowthatR isreflexive andsymmetricbutnottransitive.

Answer»

Solution :(i)`d(A,A)=0 lt 2. SO ,AR A. `
`(ii)A R Bimplies d(A,B)LT2`
`impliesd(B,A)lt 2[:' d(B,A)=d(A,B)]`
`implies B R A. `
(iii)considerthepoints `A(0,0),B(1.5,0)and C (3,0)` on thex- AXIS
then`d(A,B)1.5,D(B,C)=1.5 andd (A,C)=3.`
thereforeA RB and BRC butA, is notrelatedto C.
So, R isnot transitive .


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