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Given relations $\textsf{R(w,x)}$ and $\textsf{S(y,z)},$ the result of

SELECT DISTINCT w, x
FROM R, S

ls guaranteed to be same as $\text{R},$ if

  1. $\textsf{R}$ has no duplicates and $\textsf{S}$ is non-empty
  2. $\textsf{R}$ and $\textsf{S}$ have no duplicates
  3. $\textsf{S}$ has no duplicates and $\textsf{R}$ is non-empty
  4. $\textsf{R}$ and $\textsf{S}$ have the same number of tuples
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