Java.Core.Equals() generates an equivalence relation. What properties does such a relation have?

An equivalence relation is a relation that satisfies the following three properties:

1. Reflexivity
   • An object must be equal to itself.
   • Formally: a.equals(a)a.equals(a)a.equals(a) must return true.

String s = "hello";
System.out.println(s.equals(s)); // true

Symmetry

• If one object is equal to another, then the second must be equal to the first.
• Formally: If a.equals(b)a.equals(b)a.equals(b), then b.equals(a)b.equals(a)b.equals(a) must also be true.

String s1 = new String("hello");
String s2 = new String("hello");

System.out.println(s1.equals(s2)); // true
System.out.println(s2.equals(s1)); // true

Transitivity

• If one object is equal to a second, and the second is equal to a third, then the first must be equal to the third.
• Formally: If a.equals(b)a.equals(b)a.equals(b) and b.equals(c)b.equals(c)b.equals(c), then a.equals(c)a.equals(c)a.equals(c) must be true.

String s1 = new String("hello");
String s2 = new String("hello");
String s3 = new String("hello");

System.out.println(s1.equals(s2)); // true
System.out.println(s2.equals(s3)); // true
System.out.println(s1.equals(s3)); // true

Additional Considerations

• Consistency: If two objects are equal, equals() should always return true as long as their content does not change.
• Null Handling: A good equals() implementation should return false when compared with null.

Example in a Custom Class

To ensure that equals() follows the equivalence relation properties, a proper override should be like:

class Person {
    String name;

    Person(String name) {
        this.name = name;
    }

    @Override
    public boolean equals(Object obj) {
        if (this == obj) return true;  // Reflexivity
        if (obj == null || getClass() != obj.getClass()) return false;
        Person person = (Person) obj;
        return name.equals(person.name); // Content comparison
    }
}

This ensures reflexivity, symmetry, and transitivity, making equals() a valid equivalence relation.