select to_char(operation, 'YYYY-MM'), platform, count(*)
   from( select distinct platform, user_id, trunc(operation_time) as operation
            from Auth_Info
          .........
          )
group by to_char(operation, 'YYYY-MM'), platform
order by 1

select to_char(operation_time, 'YYYY-MM'), platform, count(distinct user_id)
            from Auth_Info
          .........
group by to_char(operation, 'YYYY-MM'), platform
order by 1

(A || B) && С - вывод 2 - Num присутствует в категории A или B и обязательно в С
(A || B) && !С - вывод 0 - Num присутствует в категории A или B и обязательно нет  в С
(A || B) || С - вывод 3 - Num присутствует в категории A или B или С

count( case when (A or B) and C then 1 end) as F1,
count( case when (A or B) and not C then 1 end) as F2,
count( case when A or B or C then 1 end) as F3

case when (A or B) and C then 2
       when (A or B) and not C then 0
       when A or B or C then 3
end as F1

with t1 as(
select to_date('01.05.2017','dd.mm.yyyy') Dat, 'A' Cat, 1 Num from dual union all
select to_date('01.05.2017','dd.mm.yyyy') Dat, 'A' Cat, 1 Num from dual union all
select to_date('01.05.2017','dd.mm.yyyy') Dat, 'A' Cat, 2 Num from dual union all
select to_date('01.05.2017','dd.mm.yyyy') Dat, 'B' Cat, 1 Num from dual union all
select to_date('02.05.2017','dd.mm.yyyy') Dat, 'C' Cat, 1 Num from dual union all
select to_date('02.05.2017','dd.mm.yyyy') Dat, 'C' Cat, 2 Num from dual union all
select to_date('02.05.2017','dd.mm.yyyy') Dat, 'C' Cat, 3 Num from dual union all
select to_date('01.04.2017','dd.mm.yyyy') Dat, 'A' Cat, 1 Num from dual )

select Count( distinct
        case listagg(Cat) within group (ORDER BY Cat) when 'BC' then Num
      end) Cnt
from 
(select distinct Decode(Cat,'A','B',Cat) Cat, Num from t1)
group by Num

select la, Count(Distinct Num) cnt
from(
select case listagg(Cat_) within group (ORDER BY Cat_) when 'BC' then '(A||B)C'
                                                     when 'B' then '(A||B)!C'
                                                     when 'C' then '(A||B)||C'
                                                     end la
,Num
from 
(select distinct Decode(Cat,'A','B',Cat) Cat_, Num from t1)
group by Num)
group by la