Step 1: Identify \(X\).
Among the isomers of \(\mathrm{C_4H_8}\), only but-2-ene exhibits cis-trans isomerism.
\[
X=\mathrm{CH_3CH=CHCH_3}
\]
Step 2: Identify the chain isomer \(Y\).
The chain isomer of but-2-ene is
\[
Y=\mathrm{(CH_3)_2C=CH_2}
\]
(2-methylpropene).
Step 3: Apply ozonolysis.
\[
\mathrm{(CH_3)_2C=CH_2}
\xrightarrow[\mathrm{Zn/H_2O}]{\mathrm{O_3}}
\mathrm{CH_3COCH_3 + HCHO}
\]
Step 4: Final conclusion.
Hence, the products formed are
\[
\boxed{\mathrm{CH_3COCH_3 + HCHO}}
\]
Therefore, the correct option is \(\boxed{(C)}\).