Math 2.0

Mathematical logic and foundations Definition

Set difference

Builds on SetElementNegation

Definition

Let AA and BB be sets. The set difference of AA and BB is the set A∖B={x∈A∣x∉B}.A \setminus B = \{x \in A \mid x \notin B\}. It is also called the relative complement of BB in AA.

Remarks

Another notation is A−BA - B. Example: {1,2,3}∖{2,4}={1,3}\{1, 2, 3\} \setminus \{2, 4\} = \{1, 3\}. The set BB need not be a subset of AA. In general, A∖B≠B∖AA \setminus B \neq B \setminus A.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

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Element, definition, no evidence levelElementdefinitionProposition, concept, no evidence levelPropositionconceptSet, definition, no evidence levelSetdefinitionNegation, definition, no evidence levelNegationdefinitionSet difference, definition, no evidence levelSet differencedefinition
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  1. Element definition
  2. Proposition concept
  3. Set definition
  4. Negation definition
  5. Set difference definition

Where this leads

7 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Complement_(set_theory), Relative complement
About this page
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MSC03E20
DefinesSet difference
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