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Relation |a-b|≤1 on Reals: Reflexive and Symmetric | JEE

JEE Maths question with a full step-by-step solution.

Question
Let RR be the relation on the set RR of all real numbers defined by a R ba\,R\,b iff ∣a−b∣≤1|a - b| \le 1. Then RR is:
AReflexive and symmetriccorrect
BSymmetric only
CTransitive only
DAnti-symmetric only
Solution
∣a−a∣=0≤1⇒R|a - a| = 0 \le 1 \Rightarrow R is reflexive. ∣a−b∣=∣b−a∣⇒R|a - b| = |b - a| \Rightarrow R is symmetric. ∣1−2∣=1≤1|1 - 2| = 1 \le 1 and ∣2−3∣=1≤1|2 - 3| = 1 \le 1, but ∣1−3∣=2>1⇒R|1 - 3| = 2 > 1 \Rightarrow R is not transitive. ∴R\therefore R is reflexive and symmetric. Correct answer: (1)
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