Relational Algebra Equivalences

• Allow us to choose different join orders and to ‘push’ selections and projections ahead of joins.

• Selections: (Cascade)

(Commute)

• Projections:

(Cascade)

• Joins:

R (S T) (R S) T

(Associative)

(R S) (S R)

(Commute)

R (S T) (T R) S

• Show that:

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