Reflexive: ∣x−x∣=0≤1, true.
Symmetric: ∣x−y∣=∣y−x∣, so symmetric.
Transitive: take x=1,y=2,z=3. ∣1−2∣=1≤1 and ∣2−3∣=1≤1, but ∣1−3∣=2>1. So not transitive.
Hence (a), (b) and (e) hold.
If R is a relation on Z (set of all integers) defined by xRy, iff |x - y| ≤ 1, then (a) R is reflexive (b) R is symmetric (c) R is transitive (d) R…
CUET UG 2022 — Mathematics Algebra
2022mcqeasy
If R is a relation on Z (set of all integers) defined by xRy, iff ∣x−y∣≤1, then
(a) R is reflexive
(b) R is symmetric
(c) R is transitive
(d) R is not symmetric
(e) R is not transitive
Choose the most appropriate answer from the options given below
Official previous-year question
Held on 30 Aug 2022 · Verified 13 Jul 2026.
Options
- A
(a) and (d) only
- B
(a), (b) and (c) only
- C
(b) and (c) only
- D
(a), (b) and (e) only
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