What is the purpose of the equals() method in Java?

The equals() method in Java is designed to compare the state of two objects for logical equality. When you use this method, it evaluates whether the attributes or fields within the objects are equivalent, rather than determining if they are the same physical instance in memory. This is particularly useful when you want to ascertain whether two distinct objects represent the same logical entity—such as two different instances of a class whose values are identical.

For instance, consider a class that represents a person. If two instances of this class are created with the same name and age, using the equals() method can help determine if they represent the same person based on those values, even though they are indeed different objects in memory.

The other choices do not accurately reflect the primary function of equals(). Checking if two objects are different instances relates to reference equality and not the content comparison that equals() performs. Comparing memory addresses refers to the default behavior of the '==' operator in Java, which checks whether two references point to the same object. Type-checking is facilitated by the instanceof operator or during method execution, but is not related to what equals() is intended to do.