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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:
$$
\begin{aligned}
& \mathrm{R}_1=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{c}, 1),(\mathrm{d}, 2)] \\
& \mathrm{R}_2=[(\mathrm{a}, 1),(\mathrm{b}, 1),(\mathrm{c}, 1),(\mathrm{d}, 1)] \\
& \mathrm{R}_3=[(\mathrm{a}, 2),(\mathrm{b}, 3),(\mathrm{c}, 2),(\mathrm{d}, 2)] \\
& \mathrm{R}_4=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{a}, 2),(\mathrm{d}, 3)], \text { then }
\end{aligned}
$$
Options:
$$
\begin{aligned}
& \mathrm{R}_1=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{c}, 1),(\mathrm{d}, 2)] \\
& \mathrm{R}_2=[(\mathrm{a}, 1),(\mathrm{b}, 1),(\mathrm{c}, 1),(\mathrm{d}, 1)] \\
& \mathrm{R}_3=[(\mathrm{a}, 2),(\mathrm{b}, 3),(\mathrm{c}, 2),(\mathrm{d}, 2)] \\
& \mathrm{R}_4=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{a}, 2),(\mathrm{d}, 3)], \text { then }
\end{aligned}
$$
Solution:
2286 Upvotes
Verified Answer
The correct answer is:
only $\mathrm{R}_4$ is not a function
We find that in $R_4, f(a)=1$ and $f(a)=2$. Hence $R_4$ is not a function.
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