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Question

Which of the following statements is not correct for the relation R defined aRb, if and only if b lives within one kilometre from a?

A
R is reflexive
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B
R is symmetric
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C
R is not anti-symmetric
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D
None of the above
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Solution

The correct option is B R is not anti-symmetric
(a,a)ϵR R is reflexive
(a,b)ϵRa lives within one kilometer from b
b lives within one kilometer from a
bRa
(a,b)ϵR(b,a)ϵR
R is symmetric
R is anti symmetric
because (a,b)ϵR & (b,a)ϵR
and ab

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