insert/delete/update in one trigger in SQL server

the am giving you is the code for trigger for INSERT, UPDATE and DELETE this works fine on Microsoft SQL SERVER 2008 and onwards database i am using is Northwind

/* comment section first create a table to keep track of Insert, Delete, Update
create table Emp_Audit(
                    EmpID int,
                    Activity varchar(20),
                    DoneBy varchar(50),
                    Date_Time datetime NOT NULL DEFAULT GETDATE()
                   );

select * from Emp_Audit*/

create trigger Employee_trigger
on Employees
after UPDATE, INSERT, DELETE
as
declare @EmpID int,@user varchar(20), @activity varchar(20);
if exists(SELECT * from inserted) and exists (SELECT * from deleted)
begin
    SET @activity = 'UPDATE';
    SET @user = SYSTEM_USER;
    SELECT @EmpID = EmployeeID from inserted i;
    INSERT into Emp_Audit(EmpID,Activity, DoneBy) values (@EmpID,@activity,@user);
end

If exists (Select * from inserted) and not exists(Select * from deleted)
begin
    SET @activity = 'INSERT';
    SET @user = SYSTEM_USER;
    SELECT @EmpID = EmployeeID from inserted i;
    INSERT into Emp_Audit(EmpID,Activity, DoneBy) values(@EmpID,@activity,@user);
end

If exists(select * from deleted) and not exists(Select * from inserted)
begin 
    SET @activity = 'DELETE';
    SET @user = SYSTEM_USER;
    SELECT @EmpID = EmployeeID from deleted i;
    INSERT into Emp_Audit(EmpID,Activity, DoneBy) values(@EmpID,@activity,@user);
end

or

Better:

IF EXISTS (SELECT * FROM inserted) AND EXISTS (SELECT * FROM deleted)
    ----Do update

IF EXISTS (SELECT * FROM Inserted) AND NOT EXISTS (SELECT * FROM deleted)

-----Do insert