Relational Algebra

Question

Comments

For 3) projection and selection are non commutative

So, 3 should be false

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i was thinking the same but then what should be the output of RHS ?

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@Utkarsh, I think output won't change.

@Srestha, Yes, they are not commutative. Bt if attributes that are included in condition c is a subset of attributes of projection operation then the query will be valid.

Answer 1

All the Statements are True 
Hence Option (d)

Comments

1 and 2 are correct. But, How is 3 correct? Suppose the condition C is applied on some attributes, say $A_{n+1}$ which is not in the projections.

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Standard results:

http://www.cs.iusb.edu/~hhakimza/B561/Lecture/Part_3f_Query_Processing_Optimization.pdf

For more refer :

https://stackoverflow.com/questions/7708293/are-selection-and-projection-associative

@ Rishabh Gupta 2

You are specifying the case that was not asked in the question.

For your query the option 3 will not hold

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only 1 and 2 are correct and 3 is not true always reason comment rishabh gupta