Relational Algebra Division -

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i'm dealing relational algebra division issue. have following 2 relations:

              | b | c                 b               --|---|--                ---               1 | 2 | 3                 2 relation r =  1 | 2 | 6   relation t =                 4 | 2 | 2               4 | 5 | 6

now i'm doing following operation: r ÷ t

when calculate this, result follows:

              | c                               --|--                              1 | 3                r ÷ t =       1 | 6                   4 | 2

for me because division @ tuples in r present in combination tuples in t. when use relational algebra calculator, such relax returns

              | c                               --|--                  r ÷ t =     4 | 2

where did make mistake? in advance help.

is there can help?

performing division on these schema not understand how operator works. definitions of operator not clear, , operation replaced combination of other operators.

a clear way see how works in case consist on create new instance of r columns ordered defining new schema: (a,c,b). is, making attribute of t appear last attribute in a. in case performing simple division, it's pretty straightforward see result, imagine if had schema r(a,d,b,c) , t(b,d). here attributes of t appear different order in r, , given instances not many tuples make difficult check looking them up.

this might difficult operator defined in relational algebra query involves concepts selection, projection , join. it's complicated put out on words. way of thinking operator, think group on sql. in example means using group attributes a,c - create groups every combination of different values these attributes appear on schema instance. each of these groups have set of values of b associated combinations of values of a, c. if think of values of attribute b in instance of t set, can verify: each group obtained grouping a,c, if set of values of b in t included in set of values of b in r, values of a,c tuple of resulting relation.

i know i'm bit late question i've seen many people confused this. if it's not clear enough, leave reference document wrote explaining more in detail , example, here.


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