JEE MATHEMATICS MCQ: RELATIONS

1 Easy

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Analyzing +4 | -1

For

\alpha \in \mathbf{N}

, consider a relation

R

\mathbf{N}

given by

R=\{(x, y): 3 x+\alpha y

is a multiple of 7

\}

. The relation

R

is an equivalence relation if and only if

View answer and explanation

Correct option: D

4 is the remainder when

\alpha

is divided by 7

Option D (4 is the remainder when α is divided by 7) is correct because it satisfies the conditions for reflexivity, symmetry, and transitivity, making R an equivalence relation.

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