| 单词 | Boolean algebra |
| 释义 | Boolean algebra (i) Both operations ∨ and ∧ are commutative and associative. (ii) 0 is an identity for addition and 1 is an identity for multiplication. (iii) Each operation ∨ and ∧ is distributive over the other. (iv) a ∨(¬a) = 1 and a ∧(¬a) = 0 for all a. For example, a power set ℘(X), where ∨ is union, ∧ is intersection, ¬ is complentation in X, and 0 is the empty set and 1 is X, is a Boolean algebra. Compare Boolean ring; see also Stone space. |
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