Q.

Let R be the relation on the set of all real numbers defined by aRb  iffa-b≤1. Then R is

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a

Reflexive and symmetric

b

Symmetric only

c

Transitive only

d

None of these

answer is A.

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Detailed Solution

a-a=0<1∴aRa∀a∈RTherefore R is reflexiveAgain aRB⇒a--b≤1 and b-a≤1⇒bRaTherefore, R is symmetric.Therefore, R is not anti-symmetric.Further, IR2 and  2R3 but 1R3,1-3=2>1Therefore, R is not transitive.
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Let R be the relation on the set of all real numbers defined by aRb  iffa-b≤1. Then R is