Which proteins are associated with institutions founded after 1880?
select t2.protein_name from institution as t1 join protein as t2 on t1.institution_id = t2.institution_id where t1.founded > 1880
And which are associated with an institution with type "Private"?
select t2.protein_name from institution as t1 join protein as t2 on t1.institution_id = t2.institution_id where t1.type = 'Private'
Union those.
select t2.protein_name from institution as t1 join protein as t2 on t1.institution_id = t2.institution_id where t1.founded > 1880 or t1.type = 'Private'
Count the union.
select count(*) from institution as t1 join protein as t2 on t1.institution_id = t2.institution_id where t1.founded > 1880 or t1.type = 'Private'