How to select specific items from table A which appear with all items of some column in table B?
I dont think there is any logical constructs like in/not in. 

But you can check array equality like below,

select id from 
(select array_agg(type)as type, id from t1  group by id) table_1 
join 
(select array_agg(type)as type from t2)table_2 
on table_1.type=table_2.type;


May be this is useful to you :)