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

JEE Main Mathematics question

Which of the following statements is not correct for the relation defined by if and only if lives within one kilometre from ?

(A) is reflexive
(B) is symmetric
(C) is anti-symmetricCorrect
(D)None of these

Answer: (C)

Solution

Reflexive: every person lives within 1 km of himself (distance 0), so holds. Symmetric: if lives within 1 km of , then lives within 1 km of — distance is the same both ways. Anti-symmetric

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Question ID VK-007328