The system that is responsible for the body's involuntary functions in the:a. Cranium.b. Central Nervous System. c. Peripheral Nervous System. d. Cervical spine.

The system that is responsible for the body's involuntary functions is the Autonomic Nervous System, which is a part of the Peripheral Nervous System. So, the correct answer is c. Peripheral Nervous System.

Here are the steps to answer this question:

1. Understand the question: The question is asking about the system that controls the involuntary functions of the body. Involuntary functions are those that we do not consciously control, such as heartbeat, digestion, and breathing.

2. Identify the options: The options given are Cranium, Central Nervous System, Peripheral Nervous System, and Cervical spine.

3. Eliminate incorrect options: The Cranium is the part of the skull that encloses the brain, so it's not a system that controls functions. The Central Nervous System includes the brain and spinal cord, and while it does control many functions, the involuntary functions are specifically controlled by the Autonomic Nervous System. The Cervical spine is a part of the spine located in the neck, so it's not a system that controls functions.

4. Choose the correct option: The Peripheral Nervous System includes all the nerves outside of the brain and spinal cord, including the Autonomic Nervous System, which controls involuntary functions. Therefore, the correct answer is the Peripheral Nervous System.