NDA 2016 Maths · Mathematics · Sets, Relations and Functions · easy

A relation R on the set of natural numbers is defined by aRb if and only if a≤ b. 1. R is reflexive. 2.

Single correct option

A relation

R

on the set of natural numbers is defined by

aRb

if and only if

a\le b

. Consider the following statements:
1.

R

is reflexive.
2.

R

is symmetric.
Which of the statements given above is/are correct?

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Answer: (A) 1 only

Since

a\le a

for every natural number

a

R

is reflexive, so statement 1 is true. But

1\le2

while

2\le1

is false, so

R

is not symmetric and statement 2 is false. The relation is, however, antisymmetric and transitive, which is a classic confusion with symmetry.

Original question written in the NDA 2016 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