Let $\mathrm{A}=[\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}], \mathrm{B}=[1,2,3]$. Relation…

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: $\begin{aligned} & \mathrm{R}_1=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{c}, 1),(\mathrm{d}, 2)] \\ & \mathrm{R}_2=[(\mathrm{a}, 1),(\mathrm{b}, 1),(\mathrm{c}, 1),(\mathrm{d}, 1)] \\ & \mathrm{R}_3=[(\mathrm{a}, 2),(\mathrm{b}, 3),(\mathrm{c}, 2),(\mathrm{d}, 2)] \\ & \mathrm{R}_4=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{a}, 2),(\mathrm{d}, 3)], \text { then } \end{aligned}$
  1. only $\mathrm{R}_3$ and $\mathrm{R}_4$ are not functions
  2. only $R_1$ and $R_2$ are not functions
  3. only $\mathrm{R}_3$ is not a function
  4. only $\mathrm{R}_4$ is not a function

Solution

We find that in $R_4, f(a)=1$ and $f(a)=2$. Hence $R_4$ is not a function.

Asked in: MHT CET 2021 (20 Sep Shift 2)

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