Final answer:
The kernel is the core of the OS, responsible for loading and operating programs, and managing Input/Output processes. It is a vital part of the system that enables communication between hardware and software and oversees essential tasks like memory and device management.
Step-by-step explanation:
The core of the operating system (OS) responsible for loading and operating programs or processes and managing Input/Output (I/O) is A) Kernel. The kernel acts as the main component of most computer operating systems. Its responsibilities include managing the system's resources and the communication between hardware and software components. It is an essential part of the system that allows for the execution of operating programs, handling system calls, and performing tasks such as process management, memory management, device management, and system server operations.
Option B) Shell is a user interface for accessing the operating system's services. Option C) BIOS stands for Basic Input/Output System, which is firmware used to perform hardware initialization during the booting process. Option D) Command Prompt is a command line interpreter application available in most Windows operating systems. It is used to execute entered commands. However, none of these is responsible for the core functions that the kernel performs.