回答編集履歴
3
「含む」の解釈の明確化
    
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            「"aaa"と"zzz"のみ含んだuser_id」の解釈が微妙ですが、aaa と zzz の両方を 
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            「"aaa"と"zzz"のみ含んだuser_id」の解釈が微妙ですが、「aaa を含む code と zzz を含む code の両方を持ち、それ以外の code (bbb や ccc など) を持たない user_id」ということなら、こんな感じでしょうか。
         
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            ```sql
         
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            create table "table" (id int primary key, user_id int, code  
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            create table "table" (id int primary key, user_id int, code text);
         
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            insert into "table" values (1, 10, 'aaa1');
         
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            insert into "table" values (2, 10, 'bbb1');
         
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追記
    
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            ```sql
         
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            insert into "table" values (14, 16, 'aaazzz');
         
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            ```
         
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            ---
         
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            追記。intersect と except でもいけますね。
         
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            ```sql
         
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            (select user_id from "table" where code like '%aaa%'
         
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             intersect
         
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             select user_id from "table" where code like '%zzz%')
         
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            except
         
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            select user_id from "table" where code not like '%aaa%' and code not like '%zzz%';
         
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            ```
         
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セミコロン追加
    
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            from "table"
         
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            where user_id in (select user_id from "table" where code like '%aaa%')
         
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              and user_id in (select user_id from "table" where code like '%zzz%')
         
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              and user_id not in (select user_id from "table" where code not like '%aaa%' and code not like '%zzz%')
         
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              and user_id not in (select user_id from "table" where code not like '%aaa%' and code not like '%zzz%');
         
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            ```
         
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            なお、aaazzz があるとそれも引っかかりますね…。
         
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