Application

Consider the following incomplete database for the PWHL with the two tables:

Team$($team$\_$name, points$)$

$\backslash$table$[[$team$\_$name,points$],[$Boston$,35],[$Montreal$,41],[$Minnesota$,35],[$New York,$26],[$Ottawa$,32],[$Toronto$,47]]$

PlayoffGame$($home$\_$team, away$\_$team, winning$\_$team$)$

$\backslash$table$[[$home$\_$team,away$\_$team,winning$\_$team$],[$Toronto$,$Minnesota,Toronto$],[$Montreal$,$Boston,Boston$],[$Minnesota$,$Toronto,Minnesota$],[$Toronto$,$Minnesota,Minnesota$],[$Minnesota$,$Boston,Minnesota$],[$Boston$,$Minnesota,Boston$]]$

$($a$)$ Translate the following query into English and give the answer returned from the query based on the data in the tables above:

$($b$)$ Express a FOL statement for the constraint that every team in the PlayoffGame table must be a listed team name in the Team table.

$($c$)$ Give a query that returns team names of playoff game winners with the least points in the league. In other words, we want all those who won a playoff game but have the least points within the set of all playoff winners. You may use the binary predicates or $=$ in your solution. Your query should still work even if we add more rows to any table.