For the chemical reactions shown below,identify the correct statement from the following:

  • A
    Compound '$A$' is a dicarboxylic acid and compound '$B$' is a diol.
  • B
    Compound '$A$' is a diol and compound '$B$' is a dicarboxylic acid.
  • C
    Both compound '$A$' and compound '$B$' are diols.
  • D
    Both compound '$A$' and compound '$B$' are dicarboxylic acids.

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The correct statement$(s)$ for the following addition reactions is(are):
$(i)$ $trans-but-2-ene \xrightarrow{Br_2/CHCl_3} M \text{ and } N$
(ii) $cis-but-2-ene \xrightarrow{Br_2/CHCl_3} O \text{ and } P$
[$A$] ($M$ and $O$) and ($N$ and $P$) are two pairs of diastereomers
[$B$] Bromination proceeds through trans-addition in both the reactions
[$C$] $O$ and $P$ are identical molecules
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