Relational Algebra

What are the Operands of Relational Algebra?

	relations (constants or variables)

What are the Operators of Relational Algebra?

	union
	intersection
	difference

	select
	project
	rename

	product
	join


















Union, Intersection, Difference

Compute the Union, Intersection, and Difference of R and S.
(remember to remove duplicates)

	R = A B
	    0 1
	    2 3

	S = A B
	    0 1
	    4 5

	R union S = A B
	  	    0 1
		    2 3
		    4 5

        R intersect S = A B
	  	      	0 1

	R - S = A B
		2 3

What must be true for Union, Intersection, Difference to be valid?

	the relations must have the same schemes (Union Compatible)


















Select

What does the Select operator do?

	extracts rows or tuples from a relation

Compute the result of the Select operation.
(What's the symbol for Select?)
     
	select[D='M' or H='9'] CDH

	C  D  H
	1  M  8
	1  W  8
	1  F  8
	2  M  9
	2  W  1
	2  F  9
	3  F  2


















Project

What does the Project operator do?

	extracts columns or attributes from a relation

Compute the result of the Project operation.
(What's the symbol for Project?)

	project[PN] SNAP

	S  N  A  P
	1  C  1	 4
	2  C  3	 4
	6  L  3  8
	2  P  5  9


















Classwork
You may work with a partner.

Evaluate the relational algebra expressions.

	select[C='1' and (G='B' or G='C')] CSG

	C  S  G
	1  1  A
	1  6  B
	2  1  C
	2  2  B
	1  3  C
	3  6  C

	project[CH] CDH

	project[D] (select[C='1'] CDH)

	C  D  H
	1  M  8
	1  W  8
	1  F  8
	2  M  9
	2  W  1
	2  F  9
	3  F  2


















Rename

Compute the result of the Rename operation.
(What's the symbol for Rename?)

	rename[S<-X](SP)

	S  P
	1  4
	6  8
	2  9

Why is Rename useful?

	1. to make relations union compatible and product compatible
	2. to make relations join on the desired attribute


















Cartesian Product

Compute the Product of R and S.
(What's the symbol for Product?)

	R = A   B
	    1   2
	    2   2

	S = C   D
	    1   1
	    2   2
	    3   3

	R x S = A   B   C   D
	        1   2   1   1
	        1   2   2   2
	        1   2   3   3
	        2   2   1   1
	        2   2   2   2
	        2   2   3   3

What must be true for the Product operation to be valid?

	the relations must have no common attribute names (Product Compatible)