Part 2 [80%-8 marks each. Queries 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 you're 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 addi- tional 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 didn't play in any matclh 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 7. Find the winner country of the match for which the very first ticket out of all the tickets in 8. Report the fname and lname of the player of the country 'Spain' with the second largest 9. Report the MID(s) of the matches for which at least two tickets were bought on the date of number of goals among all players (in any team) who play at the same position the database was purchased. If there was a tie in the match, report nothing number of goals among players of that count 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 Part 2 [80%-8 marks each. Queries 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 you're 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 addi- tional 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 didn't play in any matclh 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 7. Find the winner country of the match for which the very first ticket out of all the tickets in 8. Report the fname and lname of the player of the country 'Spain' with the second largest 9. Report the MID(s) of the matches for which at least two tickets were bought on the date of number of goals among all players (in any team) who play at the same position the database was purchased. If there was a tie in the match, report nothing number of goals among players of that count 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