To solve this problem, we need to identify the gases produced in anaerobic sludge digesters. Anaerobic digestion is a process where microorganisms break down organic matter in the absence of oxygen.$\newline$Let's analyze the options:$\newline \bullet$Option 1: Methane and CO$_2 \newline$ - Methane (CH$_4$) is a common product of anaerobic digestion.$\newline$ - Carbon dioxide (CO$_2$) is also produced during this process.$\newline$ - However, this option does not include all the gases typically produced.$\newline \bullet$Option 2: Methane, Hydrogen Sulphide and CO$_2 \newline$ - Methane (CH$_4$) is a major component of biogas produced in anaerobic digesters.$\newline$ - Hydrogen sulphide (H$_2$S) is also produced, especially when sulphur-containing compounds are present.$\newline$ - Carbon dioxide (CO$_2$) is another byproduct of the digestion process.$\newline$ - This option includes all the typical gases produced in anaerobic sludge digesters.$\newline \bullet$Option 3: Methane, Hydrogen and Oxygen$\newline$ - Methane (CH$_4$) is produced, but oxygen is not present in anaerobic conditions.$\newline$ - Hydrogen gas is not a significant product in typical anaerobic digesters.$\newline$ - This option is incorrect due to the presence of oxygen.$\newline \bullet$Option 4: Hydrogen Sulphide and Oxygen$\newline$ - Hydrogen sulphide (H$_2$S) can be produced, but oxygen is not present in anaerobic conditions.$\newline$ - This option is incorrect due to the presence of oxygen.$\newline$Based on the analysis, the correct option is Option 2: Methane, Hydrogen Sulphide and CO$_2$.