The relation $R$ defined on $A=\{1,2,3\}$ by $a R b$, if $\left|a^2-b^2\right| \leq 5$. Which of the following is false?

$R=\{(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2)\}$

JEE MATHEMATICS MCQ: RELATIONS

1 Easy

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Analyzing +4 | -1

The relation

R

defined on

A=\{1,2,3\}

a R b

, if

\left|a^2-b^2\right| \leq 5

. Which of the following is false?

View answer and explanation

Correct option: D

Range of

R=\{5\}

Option D (Range of R={5}) is false because the range of R is {1, 2, 3}, not {5}, as determined by the elements present in the relation R.

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\mathrm{Z}

R

\mathrm{N}

\mathrm{R}

\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

R

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

x

y

\}

S

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

S

X

R

X

A

B

R

R

N

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

R