The correct option is A Reflexive and symmetric
Given,
aRb if |a−b|≤1
(i) Now, |a−a|=0<1
∴aRa,∀ a∈R
Hence, R is reflexive.
(ii) If aRb⇒|a−b|≤1
⇒|b−a|≤1 (using property of modulus)
⇒bRa
Hence, R is symmetric.
(iii) We know that 1R12 and 12R1, but 12≠1
Hence, R is not anti-symmetric.
(iv)1R2 i.e. |1−2|=1 and 2R3 i.e. |2−3|=1, but 1R3 is not possible as |1−3|=2>1
Hence, R is not transitive.