15. (8 p.) Consider the following database schema which presents artists (painters), paintings, sculptures, art museums and information about which museum owns which painting. Artists(name, born, died, country) Paintings(id, name, painterName, year, type, value) Sculptures(id, name, sculptorName, year, material, value) Museums (name, city, webpage) Owns (museumName, artworkID, since, until) Suppose relations Artists, Paintings, Skulptures, Museums ja Owns have 100, 1500, 200, 40 and 100000 tuples, respectively. Give the theoretical minimum and maximum number of tuples that the results of the following expressions can have. Give also a short explanation for each result (like "if none of the sculpture ids in relation Sculptures equals to artworkID in relation Owns"). Theoretical means here that you should not think about practical issues like whether it is probable that one artist has painted such many paintings, but just theoretical limits based on the number of the tuples in each relation. It is possible that relation Artists contains artists with no paintings or sculptures in corresponding relations. a) TT name, year, value(Paintings) U7, name,year, value(Sculptures) b) Paintings > painter Name=sculptorName (Sculptures), c) Ti name(Paintings) Ti name(Sculptures) d) o material bronze (Sculptures) (Owns)