Find the minimum discerning subset in MySQL - mysql

Question

I have a t table, with let's say field1 and field2. field1 is an identifier of sets and field2 contains the member of the sets. Now, the question is, how to find out the smallest amount of field2 values that will uniquely find a given field1?
Sample data
+------+------+
|field1|field2|
| 1 | A |
| 1 | B |
| 1 | C |
| 2 | A |
| 2 | C |
| 2 | D |
| 3 | B |
| 3 | D |
+------+------+
I am looking for a query which given 1 as an argument returns (A,B), for 2 returns (A,D) or (C,D) both are good and for 3 returns (B,D). If the generic case is too hard then let's ask: is there such a pair that does this.
Once I have such a pair I can plug it into this query:
SELECT DISTINCT field1
FROM t t1
INNER JOIN t t2 USING(field1)
WHERE t1.field2 = 'A' AND t2.field2 = 'B'
and get only a single row.
I have tried something like SELECT field2 FROM t WHERE field2 NOT IN (SELECT field2 FROM t WHERE field1 != 1) and field1 = 1 but this obviously doesn't work.

Answer 1

You write a subquery that returns all pairs of field2 values for each field1. Then use a left join of this with itself, finding pairs that have the same field2 values, but different field1. These then get excluded with the NULL check, and you're left with the unique pairs for each field1.
SELECT subq1.field1, subq1.a, subq1.b
FROM (
SELECT t1.field1, t1.field2 AS a, t2.field2 AS b
FROM t AS t1
JOIN t AS t2 ON t1.field1 = t2.field1 AND t1.field2 < t2.field2
) as subq1
LEFT JOIN (
SELECT t1.field1, t1.field2 AS a, t2.field2 AS b
FROM t AS t1
JOIN t AS t2 ON t1.field1 = t2.field1 AND t1.field2 < t2.field2
) AS subq2 ON subq1.field1 != subq2.field1 AND subq1.a = subq2.a AND subq1.b = subq2.b
WHERE subq2.field1 IS NULL
DEMO

Answer 2

I have written below query
SELECT temp. field1,temp.firstValue,temp.secondValue
FROM (SELECT table1.field1 , table1.field2 firstValue ,table2.field2 secondValue FROM T table2 ,T table1
WHERE table1.field1 = table2.field1 AND table2.field2<> table1.field2 AND table1.field2 < table2.field2
) temp
GROUP BY temp. field1,temp.firstValue
It will give you below pairs
field1 firstValue secondValue
------ ---------- -----------
1 A B
1 B C
2 A C
2 C D
3 B D
Please let me know if for input 2 pair (A,C) and (A,D) would be sufficient