[Solved] How to find if a list/set is exactly within another list

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You can still use having, but test for each product — and for the absence of any other product:

SELECT o.order_id
FROM orders o
GROUP BY o.order_id
HAVING SUM( product_id = 222 ) > 0 AND
       SUM( product_id = 555 ) > 0 AND
       SUM( product_id NOT IN (222, 555) ) = 0 ;

Note that this uses the MySQL shorthand, where boolean expressions are treated as numbers with 1 for true and 0 for false. The standard syntax is:

HAVING SUM( CASE WHEN product_id = 222 THEN 1 ELSE 0 END) > 0 AND
       SUM( CASE WHEN product_id = 555 THEN 1 ELSE 0 END ) > 0 AND
       SUM( CASE WHEN product_id NOT IN (222, 555) THEN 1 ELSE 0 END ) = 0 ;

solved How to find if a list/set is exactly within another list