There could not be any class which conform to both Same type comparison and Mixed type comparison

Same-Type Comparison
With such an implementation of equals() you can store an Employee(“Hanni Hanuta”) and a Student(“Hanni Hanuta”) into the same HashSet , but retrieval from the collection will not work as expected. You will not find any of these two contained objects when you ask the HashSet whether it contains a Person(“Hanni Hanuta”) , because all three object are unequal to each other.

Mixed-Type Comparison
In a class hierarchy, where Employee and Student are subclasses of a Person , representing roles of a person, it may make sense to compare an Employee to a Student to see whether they are the same Person . With an implementation of equals() that only allows same-type comparison an Employee and a Student would not be comparable.So mixed type comparison allows comparison between parent and child object.With this type of equals() implementation you will have problems storing an Employee(“Hanni Hanuta”) and a Student(“Hanni Hanuta”) in the same HashSet . The HashSet will reject the second add() operation, because the collection already contains an element that compares equal to the new element.

Lets see an example of Mixed-Type comparison

class BaseClass {
    private int field1 = 0;

    @Override
    public boolean equals(Object obj) {
        if (obj instanceof BaseClass) {
            return field1 == ((BaseClass) obj).field1;
        }
        return false;
    }
}

class BadSubClass extends BaseClass {
    private int field2 = 0;

    @Override
    public boolean equals(Object obj) {
        if (obj instanceof BadSubClass) {
            return super.equals(obj) 
                    && field2 == ((BadSubClass) obj).field2;
        }
        return false;
    }
}

BaseClass baseClass = new BaseClass();
BadSubClass subClass = new BadSubClass();

System.out.println(baseClass.equals(subClass)); // prints 'true'
System.out.println(subClass.equals(baseClass)); // prints 'false'

Now the above implementation does not comply to symmetric property of equals
x and y, x.equals(y) should return true if and only if y.equals(x) returns true.

The work around for this is

class BaseClass {
    private int field1 = 0;

    @Override
    public boolean equals(Object obj) {
        if (obj != null && obj.getClass() == getClass()) {
            return field1 == ((BaseClass) obj).field1;
        }
        return false;
    }
}

class GoodSubClass extends BaseClass {
    private int field2 = 0;

    @Override
    public boolean equals(Object obj) {
        if (obj instanceof GoodSubClass) {
            return super.equals(obj) && field2 == ((GoodSubClass) obj).field2;
        }
        return false;
    }
}