Difference between revisions of "Set subtraction"
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Latest revision as of 00:48, 21 March 2016
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Contents
[hide]Definition
Given two sets, A and B we define set subtraction (AKA: relative complement[1]) as follows:
- A−B={x∈A|x∉B}
Alternative forms
Terminology
- Relative complement[1]
- This comes from the idea of a complement of a subset of X, say A being just X−A, so if we have A,B∈P(X) then A−B can be thought of as the complement of B if you consider it relative (to be in) A.
Notations
Other notations include:
- A∖B
Trivial expressions for set subtraction
[Expand]
Claim: (A−B)−C=A−(B∪C)
See also
References
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Categories:
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- Definitions
- Set Theory Definitions
- Set Theory
- Theorems
- Theorems, lemmas and corollaries
- Set Theory Theorems
- Set Theory Theorems, lemmas and corollaries
- Set operations
