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Logical connectives
NOT
¬
A
{\displaystyle \neg A}
,
−
A
{\displaystyle -A}
,
A
¯
{\displaystyle {\overline {A}}}
,
∼
A
{\displaystyle \sim A}
AND
A
∧
B
{\displaystyle A\land B}
,
A
⋅
B
{\displaystyle A\cdot B}
,
A
B
{\displaystyle AB}
,
A
&
B
{\displaystyle A\&B}
,
A
&
&
B
{\displaystyle A\&\&B}
NAND
A
∧
¯
B
{\displaystyle A{\overline {\land }}B}
,
A
↑
B
{\displaystyle A\uparrow B}
,
A
∣
B
{\displaystyle A\mid B}
,
A
⋅
B
¯
{\displaystyle {\overline {A\cdot B}}}
OR
A
∨
B
{\displaystyle A\lor B}
,
A
+
B
{\displaystyle A+B}
,
A
∣
B
{\displaystyle A\mid B}
,
A
∥
B
{\displaystyle A\parallel B}
NOR
A
∨
¯
B
{\displaystyle A{\overline {\lor }}B}
,
A
↓
B
{\displaystyle A\downarrow B}
,
A
+
B
¯
{\displaystyle {\overline {A+B}}}
XNOR
A
XNOR
B
{\displaystyle A\ {\text{XNOR}}\ B}
└
equivalent
A
≡
B
{\displaystyle A\equiv B}
,
A
⇔
B
{\displaystyle A\Leftrightarrow B}
,
A
⇋
B
{\displaystyle A\leftrightharpoons B}
XOR
A
∨
_
B
{\displaystyle A{\underline {\lor }}B}
,
A
⊕
B
{\displaystyle A\oplus B}
└nonequivalent
A
≢
B
{\displaystyle A\not \equiv B}
,
A
⇎
B
{\displaystyle A\not \Leftrightarrow B}
,
A
↮
B
{\displaystyle A\nleftrightarrow B}
implies
A
⇒
B
{\displaystyle A\Rightarrow B}
,
A
⊃
B
{\displaystyle A\supset B}
,
A
→
B
{\displaystyle A\rightarrow B}
converse
A
⇐
B
{\displaystyle A\Leftarrow B}
,
A
⊂
B
{\displaystyle A\subset B}
,
A
←
B
{\displaystyle A\leftarrow 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
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