JEE MATHEMATICS MCQ: RELATIONS

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Analyzing +4 | -1

Consider the following relations:

R=\{(x, y): x, y

are real numbers and

x=w y

for some rational number

w\}

S=\left\{\frac{m}{n}, \frac{p}{q}: m, n, p, q \in Z \text { such that } n, q \neq 0 \text { and } q m=p n\right\}

Then,

View answer and explanation

Correct option: A

S

is an equivalence relation but

R

is not an equivalence relation

Option A is correct. Relation S is an equivalence relation because it satisfies reflexivity, symmetry, and transitivity, while R fails to be symmetric.

More Questions from RELATIONS

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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