Relative Set Difference Operation

A relative set difference operation is a binary set difference operation that produces the set members that are in one set but not in the other set.

• AKA: RSDO, RCSO, Relative Complement Set Operation.
• Context:
• Example(s):
  • RSDO({a,b,c,d,e}, {a,c,d}) ⇒ {b,e}.
  • {a,b,c,d,e} \ {a,c,d} ⇒ {b,e}.
  • …
• Counter-Example(s):
  • an Absolute Set Difference Operation.
• See: Set Complement, Subset Operation.

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References

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Complement_(set_theory)
  • … Relative complement: If A and B are sets, then the relative complement of A in B, also known as the set-theoretic difference of B and A, is the set of elements in B, but not in A. The relative complement of A in B is denoted B ∖ A (sometimes written B − A, but this notation is ambiguous, as in some contexts it can be interpreted as the set of all b − a, where b is taken from B and a from A). Formally:
    • • B \ A = { x ∈ B | x ∉ A }.
• http://www.isi.edu/~hobbs/bgt-settheory.text
  • Set difference is defined similarly to union.

  (forall (s s1 s2)                                            (15)
          (iff (setdiff s s1 s2)
               (and (set s)(set s1)(set s2)
                    (forall (x)
                            (iff (member x s)
                                 (and (member x s1)
                                      (not (member x s2))))))))

• http://mathworld.wolfram.com/SetDifference.html

1966

• (Cohen, 1966) ⇒ Paul J. Cohen. (1966). “Set Theory and the Continuum Hypothesis” W. A. Benjamin, Inc., New York.

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