To solve this problem, we need to understand why a cockroach can live for a few days after its head is removed. Let's analyze each option:$\newline \bullet$Option 1: The cockroach does not have a nervous system.$\newline$ - This statement is incorrect. Cockroaches do have a nervous system.$\newline \bullet$Option 2: The head holds a small proportion of a nervous system while the rest is situated along the ventral part of its body.$\newline$ - This statement is correct. Cockroaches have a decentralized nervous system.$\newline$ - The majority of the nervous system is located in the ventral nerve cord, which runs along the length of the body.$\newline$ - This allows the cockroach to continue living for a short period even after the head is removed.$\newline \bullet$Option 3: The head holds a 1/3rd of a nervous system while the rest is situated along the dorsal part of its body.$\newline$ - This statement is incorrect. The nervous system is primarily ventral, not dorsal.$\newline \bullet$Option 4: The supra-oesophageal ganglia of the cockroach are situated in the ventral part of the abdomen.$\newline$ - This statement is incorrect. The supra-oesophageal ganglia are located in the head, not the abdomen.$\newline$Therefore, the correct explanation is given by Option 2: The head holds a small proportion of a nervous system while the rest is situated along the ventral part of its body.