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Public and private methods are related to the concept of encapsulation in object-oriented programming, which is about restricting the access to some of an object's components. Public methods can be accessed from any part of the program, while private methods can only be accessed within the class that they are declared in.

Public methods are functions or procedures defined within a class that can be accessed from any part of the program where the object of this class has been instantiated. They are usually called by other classes, objects, and parts of the program to execute tasks or process data. By default, methods in most programming languages are public if no access modifier is specified. For example, consider the following Python code defining a class with a public method: ```python class HelloWorld: def print_greeting(self): print("Hello, World!") ``` In this example, the `print_greeting` method is a public method because it can be accessed and executed from any part of the program that creates an object of the `HelloWorld` class.

Private methods are functions or procedures defined within a class, but they are limited in their accessibility scope. They can only be accessed and used by other methods within the same class and are not accessible from outside the class. Private methods are typically used for internal implementation details that should remain hidden from other classes and objects. In Python, private methods are denoted by using double underscore (__) as a prefix before the method name. Here's an example of a private method: ```python class Example: def __private_method(self): print("This is a private method") def public_method(self): self.__private_method() ``` In this example, the `__private_method` is a private method because it can only be accessed and executed by other methods within the `Example` class, such as the `public_method`.

Public methods are accessible from any part of the program and are typically used for tasks that need to be executed by other objects and classes. On the other hand, private methods can only be accessed within the class they are declared in and are used for implementation details that should be hidden from other classes and objects. Encapsulation, which is achieved through the use of public and private methods, enhances modularity, maintainability, and reuse of the code.