JEE MATHEMATICS MCQ: RELATIONS

1 Easy

1 of 1

Understanding +4 | -1

Let

\mathrm{A}=\{1,2,3,4\}

and let

\mathrm{R}=\{(2,2),(3,3),(4,4)

(1,2)\}

be a relation on

A

. Then

\mathrm{R}

View answer and explanation

Correct option: C

Transitive

Option C (Transitive) is correct because for the given relation R, if (a, b) and (b, c) are in R, then (a, c) is also in R. In this case, the only relevant pair is (1, 2), and there is no (2, x) in R other than (2, 2), and (1, 2) is already in R.

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