Compare two objects with .equals() and == operator

== compares object references, it checks to see if the two operands point to the same object (not equivalent objects, the same object).

If you want to compare strings (to see if they contain the same characters), you need to compare the strings using equals.

In your case, if two instances of MyClass really are considered equal if the strings match, then:

public boolean equals(Object object2) {
    return object2 instanceof MyClass && a.equals(((MyClass)object2).a);
}

...but usually if you are defining a class, there's more to equivalency than the equivalency of a single field (a in this case).

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Side note: If you override equals, you almost always need to override hashCode. As it says in the equals JavaDoc:

Note that it is generally necessary to override the hashCode method whenever this method is overridden, so as to maintain the general contract for the hashCode method, which states that equal objects must have equal hash codes.

You should override equals

 public boolean equals (Object obj) {
     if (this==obj) return true;
     if (this == null) return false;
     if (this.getClass() != obj.getClass()) return false;
     // Class name is Employ & have lastname
     Employe emp = (Employee) obj ;
     return this.lastname.equals(emp.getlastname());
 }