Final answer:
The brachial plexus is responsible for supplying the nerves to the shoulder and arm, including the axillary, radial, ulnar, and median nerves.
Step-by-step explanation:
The nerve plexus that serves the shoulder and arm is the brachial plexus. The brachial plexus is associated with the lower cervical spinal nerves and the first thoracic spinal nerve. It is responsible for sending nerve signals to the shoulder, arm, forearm, and hand. Within this plexus, the axillary nerve branches to supply the armpit region and is a key systemic nerve of the arm. The radial nerve is also a large nerve from this plexus, which alongside the ulnar nerve and the median nerve, provides innervation to various parts of the arm.