NDA 2020 Maths · Mathematics · Sets, Relations and Functions · medium

Let R be the relation on the set mathbbN defined by a R b if a divides b. Consider: 1. 2. R is antisymmetric.

Single correct option

Let

R

be the relation on the set

\mathbb{N}

defined by

a\,R\,b

a

divides

b

. Consider:
1.

R

is symmetric.
2.

R

is antisymmetric.
Which of the statements is/are correct?

Show answer and solution

Answer: (B) 2 only

2\,R\,4

but

4\,R\,2

is false, so

R

is not symmetric. If

a\mid b

and

b\mid a

for natural numbers, then

a=b

, so

R

is antisymmetric. Note

R

is also reflexive and transitive, so it is a partial order, not an equivalence relation.

Original question written in the NDA 2020 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