Introduction:
The blood of a cockroach lacks a respiratory pigment, which is a molecule responsible for carrying oxygen in the blood. This absence of a respiratory pigment in the cockroach's blood has certain implications for their respiration process.

Explanation:
1. Respiratory pigment: A respiratory pigment is a molecule found in the blood of many animals that binds to oxygen and transports it throughout the body. Hemoglobin is the most common respiratory pigment in vertebrates, while insects typically use a different respiratory pigment called hemocyanin. However, cockroaches do not possess any respiratory pigment in their blood.

2. Respiration in cockroaches: Despite the absence of a respiratory pigment, cockroaches are still capable of respiration. Their respiration process involves the following steps:
- Oxygen intake: Cockroaches have small tubes called tracheae that carry oxygen directly to their tissues. These tracheae open to the outside through small holes called spiracles located on the sides of their body segments.
- Diffusion of oxygen: Oxygen enters the cockroach's body through the spiracles and diffuses directly into the tissues. Since oxygen moves from an area of high concentration (outside the cockroach) to an area of low concentration (inside the tissues), diffusion allows oxygen to reach the cells without the need for a respiratory pigment.
- Carbon dioxide removal: Similarly, carbon dioxide produced by cellular respiration diffuses out of the tissues and is released through the spiracles.

3. Advantages and disadvantages: The absence of a respiratory pigment in cockroach blood has both advantages and disadvantages:
- Advantages: Without a respiratory pigment, cockroaches can rely solely on diffusion for oxygen transport, which is a simple and efficient process. They do not require complex circulatory systems like those found in animals with respiratory pigments.
- Disadvantages: Diffusion is not as efficient as respiratory pigments in transporting oxygen, especially over longer distances. Therefore, cockroaches may have limitations on their size and metabolic rate due to the reliance on diffusion alone.

Conclusion:
In conclusion, the absence of a respiratory pigment in the blood of a cockroach does not hinder its respiration process. Oxygen is able to enter the cockroach's tissues directly through diffusion from the environment. While this method may have limitations, it allows cockroaches to survive and carry out their metabolic processes efficiently.

Class-Insecta of phylum Arthropoda is characterised by the presence of three pairs of legs, and absence of respiratory pigments in blood, e.g. cockroach, mosquito.