Questions: Translate each of the English-language information requests below into a relational algebra query. You do not need to provide SQL or the actual output tables, though you may find it useful to compute results as you formulate relational algebra expressions. Base your answers on the following relations (see sample data on the next page): BANDS(Id, Name, FormedIn, Country) MUSICIANS(MId, Name, BandId, FromYear, ToYear) ALBUMS(AId, Title, BandId, Year) You may abbreviate relation names using just the first letter of each (B, M, A) Exercises 1. For each band, find the band ID, the name of the band, and the total number of albums listed in the database for the band. Order by album count, highest to lowest. 2. Find bands that had two or more members in the band's year of formation. List band name, year of formation, and member count. Order by band name, A-Z. 3. For each country, list the number of albums released between 1970 and 1979 (inclusive) by bands from that country. List country and album count, order by country A-Z. 4. For each band, find the span in years between the band's year of formation and the most recent album released by that band. List band name and span in years (an integer.) 5. Find the name(s) of the band(s) that released the greatest number of albums between 1970 and 1979 (inclusive)

To address question 5, we need to find the name(s) of the band(s) that released the greatest number of albums between 1970 and 1979 (inclusive). We will use relational algebra to express this query.

1. Select Albums Released Between 1970 and 1979: \[ \sigma_{1970 \leq \text{Year} \leq 1979}(A) \] This selection operation filters the ALBUMS relation to include only those albums released between 1970 and 1979.

2. Join with BANDS to Get Band Names: \[ \text{Temp1} \leftarrow \sigma_{1970 \leq \text{Year} \leq 1979}(A) \bowtie_{A.\text{BandId} = B.\text{Id}} B \] This join operation combines the filtered albums with the BANDS relation to associate each album with its corresponding band name.

3. Group by Band Name and Count Albums: \[ \text{Temp2} \leftarrow \gamma_{\text{B.Name}, \text{count}(A.AId) \rightarrow \text{AlbumCount}}(\text{Temp1}) \] This grouping operation counts the number of albums for each band and stores it in a new attribute called AlbumCount.

4. Find the Maximum Album Count: \[ \text{MaxCount} \leftarrow \gamma_{\text{max}(\text{AlbumCount})}(\text{Temp2}) \] This operation finds the maximum album count from the grouped results.

5. Select Bands with the Maximum Album Count: \[ \text{Result} \leftarrow \sigma_{\text{AlbumCount} = \text{MaxCount}}(\text{Temp2}) \] This selection operation filters the bands to include only those with the maximum album count.

The relational algebra query above identifies the band(s) that released the greatest number of albums between 1970 and 1979 by filtering, joining, grouping, and selecting based on the maximum album count. The final result will list the name(s) of the band(s) with the highest number of albums released in that decade.