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Template:Logical connectives sidebar
Logical connectives
NOT
¬
A
,
−
A
,
A
¯
,
∼
A
{\displaystyle \neg A,-A,{\overline {A},\sim A}
AND
A
∧
B
,
A
⋅
B
,
A
B
,
A
&
B
,
A
&
&
B
{\displaystyle A\land B,A\cdot B,AB,A\ \&\ B,A\ \&\&\ B}
NAND
A
∧
¯
B
,
A
↑
B
,
A
∣
B
,
A
⋅
B
¯
{\displaystyle A{\overline {\land }B,A\uparrow B,A\mid B,{\overline {A\cdot B}
OR
A
∨
B
,
A
+
B
,
A
∣
B
,
A
∥
B
{\displaystyle A\lor B,A+B,A\mid B,A\parallel B}
NOR
A
∨
¯
B
,
A
↓
B
,
A
+
B
¯
{\displaystyle A{\overline {\lor }B,A\downarrow B,{\overline {A+B}
XNOR
A
⊙
B
,
A
∨
¯
B
¯
{\displaystyle A\odot B,{\overline {A{\overline {\lor }B}
└
equivalent
A
≡
B
,
A
⇔
B
,
A
⇋
B
{\displaystyle A\equiv B,A\Leftrightarrow B,A\leftrightharpoons B}
XOR
A
∨
_
B
,
A
⊕
B
{\displaystyle A{\underline {\lor }B,A\oplus B}
└nonequivalent
A
≢
B
,
A
⇎
B
,
A
↮
B
{\displaystyle A\not \equiv B,A\not \Leftrightarrow B,A\nleftrightarrow B}
implies
A
⇒
B
,
A
⊃
B
,
A
→
B
{\displaystyle A\Rightarrow B,A\supset B,A\rightarrow B}
nonimplication (NIMPLY)
A
⇏
B
,
A
⊅
B
,
A
↛
B
{\displaystyle A\not \Rightarrow B,A\not \supset B,A\nrightarrow B}
converse
A
⇐
B
,
A
⊂
B
,
A
←
B
{\displaystyle A\Leftarrow B,A\subset B,A\leftarrow B}
converse nonimplication
A
⇍
B
,
A
⊄
B
,
A
↚
B
{\displaystyle A\not \Leftarrow B,A\not \subset B,A\nleftarrow B}
Related concepts
Propositional calculus
Predicate logic
Boolean algebra
Truth table
Truth function
Boolean function
Functional completeness
Scope (logic)
Applications
Digital logic
Programming languages
Mathematical logic
Philosophy of logic
Category
v
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