Relational Algebra Laws
Commutative and Associative Laws:
- R ⋈ S ↔ S ⋈ R, (R ⋈ S) ⋈ T ↔ R ⋈ (S ⋈ T) (natural join)
- R ∪ S ↔ S ∪ R, (R ∪ S) ∪ T ↔ R ∪ (S ∪ T)
- R ⋈Cond S ↔ S ⋈Cond R (theta join)
- σc ( σd (R)) ↔ σd ( σc (R))
Selection splitting (where c and d are conditions):
- σc∧d(R) ↔ σc ( σd (R))
- σc∨d(R) ↔ σc(R) ∪ σd(R)
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