Step 1: Analyze Reaction I.
Reaction I is the reduction of carbon monoxide ($\text{CO}$) with hydrogen ($\text{H}_2$) to form methanal (formaldehyde, $\text{HCHO}$):
\[
\text{CO}(\text{g}) + \text{H}_2(\text{g}) \xrightarrow{\text{X}} \text{HCHO}(\text{g}).
\]
This reaction is a specific hydrogenation reaction. Copper ($\text{Cu}$) catalysts are known to be selective for the formation of aldehydes and alcohols (like methanol, $\text{CH}_3\text{OH}$) from Syngas ($\text{CO}+\text{H}_2$) under certain conditions (usually lower temperatures and pressures).
The catalyst $\text{X}$ is Copper ($\text{Cu}$).
Step 2: Analyze Reaction II.
Reaction II is the complete reduction of carbon monoxide ($\text{CO}$) with hydrogen ($\text{H}_2$) to form methane ($\text{CH}_4$) and water:
\[
\text{CO}(\text{g}) + 3\text{H}_2(\text{g}) \xrightarrow{\text{Y}} \text{CH}_4(\text{g}) + \text{H}_2\text{O}(\text{g}).
\]
This reaction is known as the Sabatier reaction or methanation reaction. Nickel ($\text{Ni}$) is a highly effective and typical catalyst for the complete methanation of $\text{CO}$ (and $\text{CO}_2$) at elevated temperatures.
The catalyst $\text{Y}$ is Nickel ($\text{Ni}$).
Step 3: Conclude the final answer.
The catalysts $\text{X}$ and $\text{Y}$ are $\text{Cu}$ and $\text{Ni}$ respectively.