Division in RA

Question

Please explain me the division operation.

Considering the two relations as below,

 $R$

A	B	C
a1	b1	c1
a2	b1	c2
a1	b2	c2
a2	b2	c2
a1	b3	c3

$S$

A
a1
a2

What will be the result of $R\div S$

Comments

In table R find those value of B and C which contain both a1 and a2.

i.e. b1 and b2

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R/S : retrieve records from R , for which there exists a data which matches every record of S.

example : Π_{Sid Cid}(R)/ Π_Cid(S) : Now let suppose there are 3 entries in Cid C1,C2,C3

so output of our RA query is those Sid, that contains every Cid (C1,C2,C3).

Answer 1

We define the division operation A/B as the set of all x values  such that for every y value in (a tuple of) B, there is a tuple
<x,y> in A. 

So the relation R/S will contain only <b2,c2>

Comments

can you please specifically tell me what exactly the output will be a tuple or a column and arrangement of output in tuple and column

Answer 2

plz, refer it. R/S search all the tuples in table R for the table S which contain a1,a2.