SQL Server 2012

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create table t (A int, B int)
insert into t values (1, 1), (4, 2), (2, 1), (3, 1), (5, 2)
5 rows affected

WITH CTEA AS (
  SELECT COUNT(DISTINCT B) ac
  FROM t
  GROUP BY A
),
CTEB AS (
  SELECT COUNT(DISTINCT A) bc
  FROM t
  GROUP BY B
)
SELECT CONCAT(
         CASE WHEN MAX(bc) = 1 THEN '1' ELSE 'many' END,
         ' to ',
         CASE WHEN MAX(ac) = 1 THEN '1' ELSE 'many' END
       ) AS [A to B]
FROM CTEA
CROSS JOIN CTEB


A to B


many to 1


truncate table t;
insert into t values (1, 1), (2, 2), (5, 3)
3 rows affected

WITH CTEA AS (
  SELECT COUNT(DISTINCT B) ac
  FROM t
  GROUP BY A
),
CTEB AS (
  SELECT COUNT(DISTINCT A) bc
  FROM t
  GROUP BY B
)
SELECT CONCAT(
         CASE WHEN MAX(bc) = 1 THEN '1' ELSE 'many' END,
         ' to ',
         CASE WHEN MAX(ac) = 1 THEN '1' ELSE 'many' END
       ) AS [A to B]
FROM CTEA
CROSS JOIN CTEB


A to B


1 to 1


truncate table t;
insert into t values (2, 2), (2, 1), (2, 3)
3 rows affected

WITH CTEA AS (
  SELECT COUNT(DISTINCT B) ac
  FROM t
  GROUP BY A
),
CTEB AS (
  SELECT COUNT(DISTINCT A) bc
  FROM t
  GROUP BY B
)
SELECT CONCAT(
         CASE WHEN MAX(bc) = 1 THEN '1' ELSE 'many' END,
         ' to ',
         CASE WHEN MAX(ac) = 1 THEN '1' ELSE 'many' END
       ) AS [A to B]
FROM CTEA
CROSS JOIN CTEB


A to B


1 to many


truncate table t;
insert into t values (3, 2), (4, 2), (2, 1), (3, 1), (5, 2)
5 rows affected

WITH CTEA AS (
  SELECT COUNT(DISTINCT B) ac
  FROM t
  GROUP BY A
),
CTEB AS (
  SELECT COUNT(DISTINCT A) bc
  FROM t
  GROUP BY B
)
SELECT CONCAT(
         CASE WHEN MAX(bc) = 1 THEN '1' ELSE 'many' END,
         ' to ',
         CASE WHEN MAX(ac) = 1 THEN '1' ELSE 'many' END
       ) AS [A to B]
FROM CTEA
CROSS JOIN CTEB


A to B


many to many


truncate table t;
insert into t values (1,100),(1,100)
2 rows affected

WITH CTEA AS (
  SELECT COUNT(DISTINCT B) ac
  FROM t
  GROUP BY A
),
CTEB AS (
  SELECT COUNT(DISTINCT A) bc
  FROM t
  GROUP BY B
)
SELECT CONCAT(
         CASE WHEN MAX(bc) = 1 THEN '1' ELSE 'many' END,
         ' to ',
         CASE WHEN MAX(ac) = 1 THEN '1' ELSE 'many' END
       ) AS [A to B]
FROM CTEA
CROSS JOIN CTEB


A to B


1 to 1