IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 21

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Relations and Functions, with the answer and a step-by-step solution.

Relations and FunctionsAlgebraMultiple choiceMedium
A relation R on \mathbb{Z} is defined by aRb \Leftrightarrow a - b is divisible by 3. Which statement is correct?
  1. A
    R is reflexive and transitive, but not symmetric.
  2. B
    R is an equivalence relation.
  3. C
    R is reflexive and symmetric, but not transitive.
  4. D
    R is symmetric and transitive, but not reflexive.
Pick an option, then check.
Answer & solution

Answer: Option B

Check the three properties in turn.

Reflexive: a − a = 0, and 0 is divisible by 3, so aRa holds for every integer a. ✓

Symmetric: if a − b is divisible by 3, then b − a = −(a − b) is also divisible by 3, so bRa holds. ✓

Transitive: if a − b and b − c are both divisible by 3, then their sum a − c is divisible by 3, so aRc holds. ✓

All three hold, so R is an equivalence relation.

In fact it partitions the integers into the three remainder classes modulo 3.

Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.

Practice timed →