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NDA 2017 Maths · Mathematics · Sets, Relations and Functions · easy

Let R be the relation 'x divides y' on the set of natural numbers. 1. R is reflexive and antisymmetric. 2.

Single correct option

Let RR be the relation 'x divides y' on the set of natural numbers.

Which of the statements is/are correct?

1. RR is reflexive and antisymmetric.
2. RR is symmetric.
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

Every xx divides itself (reflexive), and x∣yx\mid y, y∣xy\mid x imply x=yx=y for naturals (antisymmetric). It is not symmetric: 2∣42\mid 4 but 4∤24\nmid 2. So only statement 1 is correct.
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Original question written in the NDA 2017 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