Consider a database schema with the following three relations:

Books$($bid: integer, bname: string, author: string, pubyear: integer, publisher: string$)$

Students$($sid: integer, sname: string, age: real, state: string$)$

Reads$($sid: integer, bid: integer, year: integer$)$

Primary keys are underlined in each relation. A book is uniquely identified by book id $($bid$).$ Additionally, every book has an id $($bid$),$ a name $($bname$),$ an author, a publication year $($pubyear$),$ and a publishing company $($publisher$).$ A student is uniquely identified by student id $($sid$).$ In addition to id$,$ each student has a name $($sname$),$ an age, and a state. If a student read a book, a record would be present in the Reads relation, with the student$$s id$,$ the book$$s id$,$ and the year the book was read.

Write the relational algebra expressions for the following queries:

Find the students who live in $$MA$$ and they are either younger than $25$ or older than $35.$

Find the oldest books $($hint: pubyear is min$).$

Find the names and authors of the newest books.

Find the names of the students who read some book in the same year when that book was published.

Find the names of the students who read all books.

Find the names and ages of the students who read all books published by $$penguin$$ publishing company in any year.