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Consider the relation $R(X Y Z)$ has the following tuples

            

X Y Z
1 2 3
1 2 4
3 2 1

_________ tuples in the result of following relational algebra expression

$(\underset{X,Y}\pi R ) \underset{R,Y < S,Y}\bowtie (\underset{S(X,Y)}\rho (\underset{Y,Z}\pi R))$

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1 2 2 3

1 2 2 4

3 2 2 3

3 2 2 4
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Initially ∏y,z(R) => Y  Z             this table is renamed as S(X,Y)  = > X   Y

                           2   3                                                                   2   3

                           2   4                                                                   2   4

                           2   1                                                                   2   1

Finally

x,y(R) natural join ∏x,y (S)

1 2 2 3

1 2 2 4

3 2 2 3

3 2 2 4

By eliminating duplicates  

So the result is 4 tuples

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