Comparing tables and getting non matching values - tsql

Question

I'm pretty new to SQL and I can't get this to work I've got these two tables below
Table A Table B
_________________ _________________
| A | 2015-10-4 | B | 2015-11-6
| B | 2015-11-4 | C | 2015-05-4
| C | 2015-05-6 | D | 2015-05-8
| D | 2015-05-7 | C | 2015-05-5
I'm trying to write a stored procedure that will get all letters from table B that has a date less than table A and any letter that doesn't exist in table B.
This is what I have so far
SELECT *
FROM A q JOIN
B c ON q.Letter = c.Letter AND q.Date > c.Date OR c.Letter IS NULL
This returns C but I can't have it return A also. It's confusing to me trying to join and compare tables still.
I do not want duplicate rows, the results I would be expecting would return
| A | 2015-10-4
| C | 2015-05-6
EDIT
I'm running into an issue now where if I have a case like this
Table A Table B
_________________ _________________
| A | 2015-10-4 | B | 2015-11-6
| B | 2015-11-4 | C | 2015-05-4
| C | 2015-05-6 | D | 2015-05-8
| D | 2015-05-7 | C | 2015-05-5
| C | 2015-05-7
It will still return C for some reason. Using a.date > max(b.date) doesn't work because max can't used that way. And I want to assume the max date can be anywhere in the table in table B.
So now my new results would be
| A | 2015-10-4
But I am getting A and C still.

Answer 1

You should use a LEFT JOIN:
SELECT DISTINCT A.letter, A.[Date]
FROM dbo.TableA A
LEFT JOIN dbo.TableB B
ON A.letter = B.letter
WHERE B.[Date] < A.[Date] OR B.letter IS NULL;
UPDATE
You should have explained your requirements as: "get all letters from table B in which every date is lesser than...."
SELECT DISTINCT A.letter, A.[Date]
FROM dbo.TableA A
LEFT JOIN (SELECT letter, MAX([Date]) [Date]
FROM dbo.TableB
GROUP BY letter) B
ON A.letter = B.letter
WHERE B.[Date] < A.[Date] OR B.letter IS NULL;

Answer 2

I would go for a UNION / UNION ALL, so that you get the result subset for the first condition + the ones for the second one.
Something similar to this should do the job:
sqlite> create table A (letter, my_date);
sqlite> create table B (letter, my_date);
sqlite> insert into A values ('A', '2015-10-04');
sqlite> insert into A values ('B', '2015-11-04');
sqlite> insert into A values ('C', '2015-05-06');
sqlite> insert into A values ('D', '2015-05-07');
sqlite> insert into B values ('B', '2015-11-06');
sqlite> insert into B values ('C', '2015-05-04');
sqlite> insert into B values ('D', '2015-05-08');
sqlite> insert into B values ('C', '2015-05-05');
A 2015-10-04
sqlite> select B.* from A, B where A.letter = B.letter and B.my_date < A.my_date UNION ALL select A.* from A where not exists (select 1 from B where B.letter=A.letter);
letter my_date
---------- ----------
C 2015-05-04
C 2015-05-05
A 2015-10-04