Using the relational schemas given below, write Relational Algebra (not SQL) queries in questions 1 to 10.

Painting (paintingId, title, artistId, year)

Artist (artistId, name, phone, country)

PaintingsForSale (paintingId,price)

Museum (museumId, museumName, city, country)

Exhibits (paintingId, musemId, fromDate, toDate)

Queries (I did the first few - but I am not sure if they are 100% correct)

1. Show the title and year of each painting.

_{(title, year)} ^(Painting)

2. Show the artist names from country, USA.

_(names)[_{(country=USA)}^(Artist)]

3. Show the titles of the paintings that had year before 1998.

_(titles)[_(year<1998)^(Painting)]

4. Show the museum names in UK that are showing the painting with id P1

5. Show the titles of the paintings, artist names and museum names and countries where they are exhibited.

6. Show the titles of the paintings and years by artist, A.Smith

7. Show the title of the oldest painting.

8. Show the titles and the artist names of the paintings with watercolor medium.

9. Show the names of museums with no exhibits.

10. Show the title of the painting with the highest price.