Relational Algebra

Question

0

in a) projection has subscript hid and first select has hCity="Vancouver" and second select has year =2005 as subscript

in b) projection has subscript hid and select has hCity="Vancouver" ^ year is not equal to 2005 as subscript

In second question first projection operator has subscript s_name, title and second projection operaor has title as its subscript

Schema for second-

book(acc_no,yr_pub,title)

user(card_no,b_name,b_address)

supplier(s_name, s_adder)

borrow(acc_no, card_no,doi)

supp(acc_no, s_name, price,dos)

Answer 1

Option B select id of Hotels which are not booked in year 2005 but it will not select those hotels which are not even booked..
If Natural Join replaced by cross product then result must be same as option A.

Option A already gives hotels id which are not booked in year 2005..

Answer 2

answer will be c option 

explanation:-  in option (a) ^id(sigm_{hcity="vancour"(hotel)) gives table which contain all the hid which hav hcity ="vancouver"} 

hid

pie_id(sigma_year=2005 (booking)) it gives table containing atrribute HID with element year =2005

HID

  if we subtract 2nd from 1st then it will give table with attribute HID with element year !=2005

HID

in (b) option (sigma_{hcity='vancour'^year!=2005}(booking(natural join)hotel)) gives table with cartesian product booking and hotel with attribute(gid,hid,hname,h address,h_city,room_no,from_date,year,no_of_days)  but year value doesnot = 2005

when we apply pie_id on that it will give required answer so both answer will be right 

Comments

But as suggested by @laser second will not give those hotels which were not booked at all

Answer 3

in second question sigma_{card_no=753}(borrow(natural join)book) gives table containing attributes(yr_pub,title,cc_no,card_no,doi) after applying pie_title it gives table containing only title atttribute under card no =753                                       (second algebra)

now pie_{s_name,title}(supply(natural join)book) gives table with attribute(s_name,title) containing all the supplier name and title       (first algebra)

now we divide first by second then it will give only those supplier name where title name of second matches with title name first thus it will provide name of all the suppliers who supplied all the copies of book under card-no =753

Comments

so which is the correct option ??

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option c is correct

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for both question answer will be (c)