On the set $N$ of all natural numbers define the relation $R$ by $ a R b$ if and only if the G.C.D. of $a$ and $b$ is 2 . then $R$ is

Reflexive, symmetric and transitive

JEE MATHEMATICS MCQ: RELATIONS

1 Easy

1 of 1

Analyzing +4 | -1

On the set

N

of all natural numbers define the relation

R

a R b

if and only if the G.C.D. of

a

and

b

is 2 . then

R

View answer and explanation

Correct option: B

Symmetric only

Option B (Symmetric only) is correct because if the GCD of a and b is 2, then the GCD of b and a is also 2, but a number's GCD with itself is itself, and transitivity doesn't hold.

More Questions from RELATIONS

Practice All Chapter MCQs →

In the set

\mathrm{Z}

of all integers, which of the following relation

R

is not an equivalence relation? Let

\mathrm{N}

denote the set of all natural numbers and

\mathrm{R}

be the relation on

\mathrm{N} \times \mathrm{N}

defined by

(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})

a d(b+c)=b c(a+d)

, then

\mathrm{R}

is Let

W

denote the words in the English dictionary. Define the relation

R

by:

R=\{(x, y) \in W \times W \mid

the words

x

and

y

have at least one letter in common

\}

Let

S

be the set of all real numbers. Then, the relation

R = \{ \left( {a,\;b} \right):1 + ab > 0\}

S

is Let

X

be a family of sets and

R

be a relation on

X

defined by '

A

is disjoint from

B

'. Then

R

is:

R

is relation on

N

given by

R = \left\{ {\left( {x,\;y} \right):4x + 3y = 20} \right\}

. Which of the following belongs to

R