Class

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There are several definitions of a class in use. The following definition is given by Copi. [1] An ordered 4-tuple (C,(∩,∪),~,(1,0)) is called a class if it satisfies the following axioms.
1\. (C, ∩, 1) is an abelian monoid
2\. (C, ∪, 0) is an abelian monoid
3\. 0 ≠ 1
4\. for every a in C,

* a ∩ ~a = 0
* a ∪ ~a = 1

5\. and for every a, b, and c in C,

* a ∪ (b ∩ c) = (a ∪ b) ∩ (a ∪ c)
* a ∪ (b ∩ c) = (a ∩ b) ∪ (a ∩ c).

## References

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1. ↑ Symbolic Logic. Fifth edition. Pages 175-176.