Q.Using the sports database containing two relations (TEAM, MATCH_DETAILS), answer the following relational algebra queries.

Selection = WHERE, projection = the SELECT list, rename = ALTER TABLE ... RENAME. On the given data:

-- a) both > 70            -> M1
-- b) first < 70, second>70 -> M5
-- c) Team 1 won (played as first OR second):
WHERE (FirstTeamID=1 AND FirstTeamScore>SecondTeamScore)
   OR (SecondTeamID=1 AND SecondTeamScore>FirstTeamScore);   -- M1, M3
-- d) Team 2 did not win (flip the comparison)               -- M1, M4
ALTER TABLE TEAM RENAME TO T_DATA;                            -- e)
ALTER TABLE T_DATA RENAME COLUMN TeamID  TO T_ID; …

In relational-algebra terms: selection (choosing rows by condition) becomes WHERE, projection (choosing columns) becomes the SELECT list, and rename (the rho operation) becomes ALTER TABLE ... RENAME. Data used (MATCH_DETAILS): M1 1v2 90-86, M2 3v4 45-48, M3 1v3 78-56, M4 2v4 56-67, M5 1v4 32-87, M6 2v3 67-51.

a) Matches where both teams scored more than 70

SELECT MatchID
FROM MATCH_DETAILS
WHERE FirstTeamScore > 70 AND SecondTeamScore > 70;

Only M1 qualifies (90 and 86). AND demands both conditions hold — M5's 87 fails because its partner score is 32.

b) FirstTeam scored below 70, SecondTeam above 70

SELECT MatchID
FROM MATCH_DETAILS
WHERE FirstTeamScore < 70 AND SecondTeamScore > 70;

M5 alone: 32 < 70 and 87 > 70.

c) Matches played by Team 1 and won by it

Team 1 can appear as either the first or the second team, so the win test has two branches joined by OR:

SELECT MatchID, MatchDate
FROM MATCH_DETAILS
WHERE (FirstTeamID = 1 AND FirstTeamScore > SecondTeamScore)
   OR (SecondTeamID = 1 AND SecondTeamScore > FirstTeamScore);

Team 1 played M1 (won 90-86), M3 (won 78-56) and M5 (lost 32-87) — the WHERE keeps only the wins.

d) Matches played by Team 2 and NOT won by it

Same two-branch shape, with the comparison flipped to "scored less":

SELECT MatchID
FROM MATCH_DETAILS
WHERE (FirstTeamID = 2 AND FirstTeamScore < SecondTeamScore)
   OR (SecondTeamID = 2 AND SecondTeamScore < FirstTeamScore);

Team 2's matches: M1 (86 vs 90 — lost), M4 (56 vs 67 — lost), M6 (67 vs 51 — won, so excluded). …