What methods can be used to determine the equality of two objects in Java?

In Java, equality of two objects can be determined in several ways:

1. Operator == — compares references to objects, i.e., checks whether both variables point to the same object in memory.

2. Method equals() — intended for checking logical equality of objects. By default (in the Object class), it behaves like ==, but it is often overridden to compare the contents of objects.

Example of overriding equals():

class Person {
    private String name;
    private int age;

    public Person(String name, int age) {
        this.name = name;
        this.age = age;
    }

    @Override
    public boolean equals(Object obj) {
        if (this == obj) return true;
        if (obj == null || getClass() != obj.getClass()) return false;
        Person other = (Person) obj;
        return age == other.age && name.equals(other.name);
    }

    @Override
    public int hashCode() {
        return Objects.hash(name, age);
    }
}

3. Use of specialized methods or libraries — for example, Objects.equals() for safe comparison considering null.

Important: when overriding equals(), you should also override hashCode() for correct operation in collections.