Internal Operations on LIMIT & OFFSET clause

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Hi Friends,

       I have one doubt in LIMIT & OFFSET clause operation.
I have a table "test_limit",  and it contain,

SELECT * from test_limit;
s_no |    name
------+-------------
   1 | anbarasu
   8 | egambaram
  12 | jyothi
   6 | mahalakshmi
   4 | maheswari
   2 | manju
   5 | ramkumar
   7 | sangeetha
  11 | sasikala
  10 | thekkamalai
   9 | vivek
  13 | ganeshwari
   3 | anandhi
(13 rows)

Here, I applied LIMIT clause as bellow.
SELECT * from test_limit LIMIT 5;
s_no |    name
------+-------------
   1 | anbarasu
   8 | egambaram
  12 | jyothi
   6 | mahalakshmi
   4 | maheswari
(5 rows)

In this above query was processed only five records  OR all the 13 record
was got and then only 5 record printed.
this is what my doubt.

I tried where clause in above query as bellow.
SELECT * from test_limit where s_no IN (1,2,3,4,5,6,7,8,9) LIMIT 5;
s_no |    name
------+-------------
   1 | anbarasu
   8 | egambaram
   6 | mahalakshmi
   4 | maheswari
   2 | manju
(5 rows)

In this case It should process up to  records fulfill the requirement.
i.e  atleast it should process 6 records.
My question is it is processed only 6 records (fulfill the requirement) or
all (13) the records.

I also tried ORDER BY clause as bellow.
SELECT * from test_limit ORDER BY s_no LIMIT 5;
s_no |   name
------+-----------
   1 | anbarasu
   2 | manju
   3 | anandhi
   4 | maheswari
   5 | ramkumar
(5 rows)


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