On the set $N$ of natural numbers, define the relation $R$ by $a$ $R$ $b$ iff the GCD of $a$ and $b$ is 2, then $R$ is

Neither reflexive, nor symmetric and transitive.

JEE MATHEMATICS MCQ: RELATIONS

1 Easy

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Analyzing +4 | -1

On the set

N

of natural numbers, define the relation

R

a

R

b

iff the GCD of

a

and

b

is 2, then

R

View answer and explanation

Correct option: B

Symmetric only

The correct answer is B. The relation

R

is symmetric only because if the GCD of

a

and

b

is 2, then the GCD of

b

and

a

is also 2, but it's not reflexive or transitive.

Practice All Chapter MCQs →

\mathrm{Z}

R

\mathrm{N}

\mathrm{R}

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

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

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

\mathrm{R}

W

R

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

x

y

\}

S

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

S

X

R

X

A

B

R

R

N

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

R