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select @@version;
(No column name)
Microsoft SQL Server 2022 (RTM) - 16.0.1000.6 (X64)
Oct 8 2022 05:58:25
Copyright (C) 2022 Microsoft Corporation
Express Edition (64-bit) on Windows Server 2019 Standard 10.0 <X64> (Build 17763: ) (Hypervisor)
CREATE TABLE TableA
(
DOB VARCHAR(512)
);

INSERT INTO TableA (DOB) VALUES
('1994-04-12'),
('1996-12-06'),
('2009-11-22');

SELECT * FROM TableA
DOB
1994-04-12
1996-12-06
2009-11-22
CREATE TABLE TableB
(
Start VARCHAR(512),
cutoff VARCHAR(512)
);

INSERT INTO TableB (Start, cutoff) VALUES
('1990-01-01', '1999-12-31'),
('2000-01-01', '2009-12-31');

SELECT * FROM TableB
Start cutoff
1990-01-01 1999-12-31
2000-01-01 2009-12-31
SELECT *
FROM TableA A
INNER JOIN TableB B on A.DOB BETWEEN B.Start and B.Cutoff
DOB Start cutoff
1994-04-12 1990-01-01 1999-12-31
1996-12-06 1990-01-01 1999-12-31
2009-11-22 2000-01-01 2009-12-31