Let $R$ be a relation defined on $N$ as a $R b$ if $2 a+3 b$ is a multiple of $5, a, b \in N$. Then $R$ is

JEE MATHEMATICS MCQ: RELATIONS

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Analyzing +4 | -1

Let

R

be a relation defined on

N

as a

R b

2 a+3 b

is a multiple of

5, a, b \in N

. Then

R

View answer and explanation

Correct option: A

an equivalence relation

Option A (an equivalence relation) is correct because the relation R satisfies the reflexive, symmetric, and transitive properties.

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\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