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NDA 2021 Maths · Mathematics · Sets, Relations and Functions · medium

The relation aRbiff a-b is divisible by 3 on the set of integers is an equivalence relation. 2. The relation 'a divides b' on the set of natural…

Single correct option

Which of the statements is/are correct? 1. The relation aRb  ⟺  a−baRb\iff a-b is divisible by 33 on the set of integers is an equivalence relation. 2. The relation 'aa divides bb' on the set of natural numbers is symmetric.
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
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Answer: (A) 1 only

Statement 1: congruence modulo 3 is reflexive, symmetric and transitive. Statement 2: 22 divides 44 but 44 does not divide 22, so the divisibility relation is not symmetric (it is reflexive, antisymmetric and transitive). Only 1 is correct.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake