postgresql - Simplify and/or optimize sql query with INTERSECT or HAVING -

i have following data:

 tag_id | taggable_id  --------+-------------       1 |           1       2 |           1       3 |           1       4 |           1       1 |           2       2 |           2       5 |           2       6 |           2       7 |           3       8 |           3       9 |           3      10 |           3 

and want bring taggable_ids in group of tag_ids , in group , another... (max 4 groups).
example:

• if search taggable_ids tag_id 1 or 7 , tag_id 4 should return 1
• if search taggable_ids tag_id 1 , tag_id 6 , tag_id 2 or 8 should return 2
• if search taggable_ids tag_id 8 , tag_id 5 should not return ids

in gross way(for second example), query following:

select taggable_id taggings tag_id in (1) intersect select taggable_id taggings tag_id in (6) intersect select taggable_id taggings tag_id in (2,8) 

i think simplifying it, looks like:

select taggable_id taggings tag_id in (1,2,6,8) group taggable_id having count(*)=3 

but i'm wondering if can done in simpler way. thoughts?

this can cast case of relational division. have assembled arsenal of query techniques under related question:

• how filter sql results in has-many-through relation

depending on data distribution , other factors, may fastest:

select distinct taggable_id   taggings t1 join   taggings t2 using (taggable_id) join   taggings t3 using (taggable_id)  t1.tag_id = 1 ,    t2.tag_id = 6 ,    t3.tag_id in (2, 8); 

assuming unique (tag_id, taggable_id), distinct not needed example. might necessary other (list) predicates.

sql fiddle (building on @clodoaldo's, thanks).