Final answer:
The peripheral nervous system is indeed responsible for both sending and receiving signals between the brain and the rest of the body, making the statement true.
Step-by-step explanation:
The statement that the peripheral nervous system is responsible for both sending and receiving signals to and from the brain is true. The peripheral nervous system (PNS) includes both the autonomic nervous system, which controls involuntary actions, and the sensory-somatic nervous system. The sensory-somatic nervous system transmits information from the skin, muscles, and sensory organs to the central nervous system, and motor information is sent from the central nervous system to the muscles.
Through its extensive network of nerves, the PNS connects the central nervous system (CNS), consisting of the brain and spinal cord, to the rest of the body, functioning like the wires connecting a power plant to individual houses, both delivering the CNS's commands and reporting sensory information back to it.