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逻辑或 .
文氏图
A
∨
B
{\displaystyle A\lor B}
逻辑或 (logical or)又称逻辑析取 (logical disjunction)、逻辑选言 ,是逻辑 和数学 概念中的一个二元逻辑算符。其运算方法是:如果其两个变量中有一个真值为“真”,其结果为“真”,两个变量同时为假,其结果为“假”。
定义
逻辑或 是两个逻辑变量的一种运算,经常是两个命题的运算。它满足:当且仅当其两个变量的真值都为假时,其结果为假。
A或B 的真值表(也写作A
∨
{\displaystyle \lor }
B (逻辑学),A || B (计算机科学),或A + B (电子学))。
A
B
∨
真
真
真
真
假
真
假
真
真
假
假
假
计算机科学中的运用
位运算
逻辑或 常在位运算 中使用,比如:
0 or 0 = 0
0 or 1 = 1
1 or 0 = 1
1 or 1 = 1 or
运算符可以用来将比特域中的位设定为1,方法是把此域和一个各位均为1的常量域取逻辑或运算。
编程中的使用
逻辑运算
并集运算
x ∈ A ∪ B ⇔( 当且仅当) (x ∈ A ) ∨ (x ∈ B ).
自然语言
就如其他在数理逻辑中形式化的概念一般,自然语言中的“或”和逻辑的“或”高度相关,但有差异。像例如在“你给我打电话,或者寄信给我”这例子中,其真实的意思往往是“你要不就给我打电话,要不就给我寄信,但不要同时寄信和打电话。”,也就是会排除掉两者皆成立的状况;在另一方面,在“小橘子姐姐开赛车的驾驶技术神乎其技,因此她很努力,或者她很有天分”这例子中,两者皆成立的状况通常并未排除。也就是说,在自然语言中,“或”可以指“逻辑或”,或者是“逻辑异或 ”。
相关网页
恒真 (
⊤
{\displaystyle \top }
)
与非 (
↑
{\displaystyle \uparrow }
)
反蕴涵 (
←
{\displaystyle \leftarrow }
)
蕴涵 (
→
{\displaystyle \rightarrow }
)
或 (
∨
{\displaystyle \lor }
)
非 (
¬
{\displaystyle \neg }
)
异或 (
⊕
{\displaystyle \oplus }
)
双条件 (
↔
{\displaystyle \leftrightarrow }
)
命题
或非 (
↓
{\displaystyle \downarrow }
)
非蕴涵 (
↛
{\displaystyle \nrightarrow }
)
反非蕴涵 (
↚
{\displaystyle \nleftarrow }
)
与 (
∧
{\displaystyle \land }
)
恒假 (
⊥
{\displaystyle \bot }
)
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