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Relational Algebra Laws (cont)

Selection pushing   ( σc(R ∪ S) and σc(R ∪ S) ):
  • σc(R ∪ S)  ↔  σcR ∪ σcS,   σc(R ∩ S)  ↔  σcR ∩ σcS
Selection pushing with join ...
  • σc (R ⋈ S)   ↔   σc(R)  ⋈  S    (if c refers only to attributes from R )
  • σc (R ⋈ S)   ↔   R  ⋈  σc(S)    (if c refers only to attributes from S )
If c refers to attributes from both R and S:
  • σc′∧c″ (R ⋈ S)   ↔   σc′(R)  ⋈  σc″(S)
  • c′ contains only R attributes, c″ contains only S attributes