Let A=[a, b, c, d], B=[1,2,3] . Relation R_1, R_2, R_4 are as follows: aligned & R _ 1 =[( a,1),( b,2),( c,1),( d,2)] and R _ 2 =[(a,1),(b,1),(c,1),(d,1)] and R _ 3 =[( a,2),( b,3),( c,2),( d,2)] and R _ 4

Correct answer: D. only R_4 is not a function We find that in R_4, f(a)=1 and f(a)=2 . Hence R_4 is not a function.

JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Sets and Relations

JEE Main · Mathematics · Sets and Relations

Let A=[a, b, c, d], B=[1,2,3] . Relation R_1, R_2, R_4 are as...

Let

\mathrm{A}=[\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}], \mathrm{B}=[1,2,3]

. Relation

\mathrm{R}_1, \mathrm{R}_2, \mathrm{R}_4

are as follows:

\begin{aligned}& \mathrm{R}}_{1}=[( \mathrm{a},1),( \mathrm{b},2),( \mathrm{c},1),( \mathrm{d},2)] \\ \text{ and } \mathrm{R}}_{2}=[(\mathrm{a},1),(\mathrm{b},1),(\mathrm{c},1),(\mathrm{d},1)] \\ \text{ and } \mathrm{R}}_{3}=[( \mathrm{a},2),( \mathrm{b},3),( \mathrm{c},2),( \mathrm{d},2)] \\ \text{ and } \mathrm{R}}_{4}=[(\mathrm{a},1),(\mathrm{b},2),(\mathrm{a},2),(\mathrm{d},3)], \text { then } \end{aligned}

Options

Aonly $\mathrm{R}_3$ and $\mathrm{R}_4$ are not functions
Bonly $R_1$ and $R_2$ are not functions
Conly $\mathrm{R}_3$ is not a function
Donly $\mathrm{R}_4$ is not a function

Correct answer

D. only $\mathrm{R}_4$ is not a function

Step-by-step solution

We find that in

R_4, f(a)=1

and

f(a)=2

. Hence

R_4

is not a function.

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