Postgres 12

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CREATE TABLE mytable(
   ID   INT  NOT NULL 
  ,Flag BOOLEAN 
);
INSERT INTO mytable(ID,Flag) VALUES (1,True);
INSERT INTO mytable(ID,Flag) VALUES (1,True);
INSERT INTO mytable(ID,Flag) VALUES (1,NULL);
INSERT INTO mytable(ID,Flag) VALUES (1,True);
INSERT INTO mytable(ID,Flag) VALUES (1,NULL);
INSERT INTO mytable(ID,Flag) VALUES (2,False);
INSERT INTO mytable(ID,Flag) VALUES (2,False);
INSERT INTO mytable(ID,Flag) VALUES (2,False);
INSERT INTO mytable(ID,Flag) VALUES (2,NULL);
INSERT INTO mytable(ID,Flag) VALUES (2,NULL);

CREATE TABLE

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

INSERT 0 1

update mytable t
set flag = (
    select bool_or(flag) from mytable t1 where t1.id = t.id
)

UPDATE 10

select * from mytable

id
flag

1
t

1
t

1
t

1
t

1
t

2
f

2
f

2
f

2
f

2
f

SELECT 10