mysql left join, limit and sorting

I've a doubt. I need to make a left join between two tables and get only the first result (I mean the first record on table A that 开发者_JAVA百科doesn't match nothing on table B). This is an example

create table a (
id int not null auto_increment primary key,
name varchar(50),
surname varchar(50),
prov char(2)
) engine = myisam;

insert into a (name,surname,prov)
values ('aaa','aaa','ss'),('bbb','bbb','ca'),('ccc','ccc','mi'),('ddd','ddd','mi'),('eee','eee','to'),
       ('fff','fff','mi'),('ggg','ggg','ss'),('hhh','hhh','mi'),('jjj','jjj','ss'),('kkk','kkk','to');


create table b (
id int not null auto_increment primary key,
id_name int
) engine = myisam;

insert into b (id_name) values (3),(4),(8),(5),(10),(1);

Query A:

select a.*
from a
left join b
on a.id = b.id_name 
where b.id_name is null and a.prov = 'ss'
order by a.id
limit 1

Query B:

select a.*
from a
left join b
on a.id = b.id_name 
where b.id_name is null and a.prov = 'ss'
limit 1

Both queries gives me right result, that is record with id = 7. I want to know if I can rely on query B even without specifing sorting on id or if it's just a case that I get the right result.

I ask that because on large recordset (more than 10 millions of rows), the query without sorting gives me one record immediately while applying sorting it takes even more than 20 seconds even though a.id is primary key.

Thanks in advance.

---

You can't rely on query B. Mysql just returned what it found faster to return.

---

Is there an index on table "b" on column "id_name"? If no, then create it and tell us what You get (I mean how fast) It doesn't matter You are looking for not matched rows, JOIN has to be made before it can test if there is match or not.