Team(country, coach) A tuple in this relation represents the team of a country that participates in the competition. country is the teams country name, and coach is the name of the teams coach.

Player(PID, fname, lname, position, goals, country) A tuple in this relation represents a football player who is participating in the contest. PID is the players ID, fname is their first name, lname is their last name, position is the position they are playing on the pitch, goals is the number of goals the player has scored so far in the competition, and country is the country of the team they are playing for.

Stadium(SID, capacity, city) A tuple in this relation represents a stadium where a match takes place. SID is the stadiums ID, capacity is the capacity of the stadium, and city is the city where the stadium is located.

Match(MID, date, time, SID) A tuple in this relation represents a match. MID is the id of the match, date is the date the match is scheduled on, time is the time the match is scheduled on, and SID is the SID of the stadium where the match takes place.

Ticket(TID, dateIssued, timeIssued, MID) A tuple in this relation represents a ticket that was purchased. TID is the tickets id, dateIssued is the date that it was purchased, timeIssued is the time that it was purchased, and MID is the MID of the match it was purchased for. 1

Competes(MID, country1, country2, goals1, goals2) A tuple in this relation represents which teams are competing in a match. MID is the id of the match, country1 is the country of the first team, country2 is the country of the second team, goals1 is the number of goals scored by the first team, and goals2 is the number of goals scored by the second team.

Integrity constraints

Player[country] Team[country]

Match[SID] Stadium[SID]

Ticket[MID] Match[MID]

Competes[MID] Match[MID]

Competes[country1] Team[country]

Competes[country2] Team[country]

write the queries below in relational algebra. There are a number of variations on relational algebra, and different notations for the operations. You may use only the operations defined in Section 2.4 of the text and you must use the same notation as in the textbook. In particular, assume all relations are sets (not bags), and do not use any of the extended relational algebra operations from Chapter 5 (for example, do not use the extended projection). Some of the queries cannot be expressed in the language that you are using. In those cases, simply write cannot be expressed. Later in the course, when we learn SQL, it will be interesting to consider whether they can be expressed in SQL. You are encouraged to use the assignment operator (:=) to define intermediate results, and it is a good idea to add commentary explaining what youre doing before each expression. This way, even if your final answer is not completely correct, you may receive partial marks. You should assume that both the original constraints enforced by the schema and the additional ones given in Part 1 hold for the following queries. However, do not make any assumptions other than those. Your queries should work for any database that satisfies those constraints. Note: These queries are not in order according to difficulty.

1. Report the country of the team that has played in every stadium. If there are ties report all of them.

2. Report the MID of the match for which the highest number of tickets was purchased. If there are ties report all of them.

3. Report the PID(s) of the player(s) of the team(s) that didnt play in any match.

4. Report the SID(s) of the stadium(s) where exactly one match took place.

5. Report the coaches of the teams with the highest difference in the number of goals when competed with each other at a match. If there are ties, report all of them.

6. Report the fname and lname of the players whose position is D and have scored the largest number of goals among all players (in any team) who play at the same position.

7. Find the winner country of the match for which the very first ticket out of all the tickets in the database was purchased. If there was a tie in the match, report nothing.

8. Report the fname and lname of the player of the country Spain with the second largest number of goals among players of that country.

9. Report the MID(s) of the matches for which at least two tickets were bought on the date of the match.

10. Consider all teams that have won at least one match. For each of these teams, report its country, the position of its player with the largest number of goals and the number of goals he/she has scored.