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JEE MATHEMATICS MCQ: RELATIONS

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A relation

R_1

defined on a set of real number

R

as

a R, b \Leftrightarrow a^2+b^2=1

. Relation

R_2

defined on set of natural number

{N}

such that

(a, b) R_2,(c, d) \Leftrightarrow a+b=c+d

that

View answer and explanation

Correct option: B

R_1

is not reflexive,

R_2

is reflexive

Option B (

R_1

is not reflexive,

R_2

is reflexive) is correct because

R_1

requires

a^2 + a^2 = 1

which is not true for all real numbers, while

R_2

satisfies the reflexive property.

More Questions from RELATIONS

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\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}

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

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

\mathrm{R}

W

denote the words in the English dictionary. Define the relation

R

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

x

y

have at least one letter in common

\}

S

be the set of all real numbers. Then, the relation

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

S

X

be a family of sets and

R

be a relation on

X

A

is disjoint from

B

R

R

N

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

. Which of the following belongs to

R