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JEE MATHEMATICS MCQ: RELATIONS

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Analyzing +4 | -1

Among the relations

\begin{array}{l} S=\left\{(a, b): a, b \in \mathbb{R}-\{0\}, 2+\frac{a}{b} > 0\right\} \text { and } \\ T=\left\{(a, b): a, b \in \mathbb{R}, a^{2}-b^{2} \in \mathbb{Z}\right\},\end{array}

View answer and explanation

Correct option: D

T

is symmetric but

S

is not

Option A (

(-\infty,-\frac{21}{4}] \cup[0, \infty)

) is correct because by finding the range of the function, we get

y \in(-\infty,-\frac{21}{4}] \cup[0, \infty)

.

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