Editing Logical connective (section)

===List of common logical connectives===
Commonly used logical connectives include the following ones.<ref name="chao2023">{{cite book |last1=Chao |first1=C. |title=数理逻辑：形式化方法的应用 |trans-title=Mathematical Logic: Applications of the Formalization Method |date=2023 |publisher=Preprint. |location=Beijing |pages=15–28 |language=Chinese}}</ref> 
* [[negation|Negation (not)]]: <math>\neg</math>, <math>\sim</math>, <math>N</math> (prefix) in which <math>\neg</math> is the most modern and widely used, and <math>\sim</math> is also common;
* [[logical conjunction|Conjunction (and)]]: <math>\wedge</math>, <math>\&</math>, <math>K</math> (prefix)  in which <math>\wedge</math> is the most modern and widely used;
* [[logical disjunction|Disjunction (or)]]: <math>\vee</math>, <math>A</math> (prefix)  in which <math>\vee</math> is the most modern and widely used;
* [[Material conditional|Implication (if...then)]]: <math>\to</math>, <math>\supset</math>, <math>\Rightarrow</math>, <math>C</math> (prefix)  in which <math>\to</math> is the most modern and widely used, and <math>\supset</math> is also common;
* [[Logical biconditional|Equivalence (if and only if)]]: <math>\leftrightarrow</math>, <math>\subset\!\!\!\supset</math>,  <math>\Leftrightarrow</math>, <math>\equiv</math>, <math>E</math> (prefix) in which <math>\leftrightarrow</math> is the most modern and widely used, and <math>\subset\!\!\!\supset</math> is commonly used where <math>\supset</math> is also used.

For example, the meaning of the statements ''it is raining'' (denoted by <math>p</math>) and ''I am indoors'' (denoted by <math>q</math>) is transformed, when the two are combined with logical connectives:
* It is '''''not''''' raining (<math>\neg p</math>);
* It is raining '''''and''''' I am indoors (<math>p \wedge q</math>);
* It is raining '''''or''''' I am indoors (<math>p \lor q</math>);
* '''''If''''' it is raining, '''''then''''' I am indoors (<math>p \rightarrow q</math>);
* '''''If''''' I am indoors, '''''then''''' it is raining (<math>q \rightarrow p</math>);
* I am indoors '''''if and only if''''' it is raining (<math>p \leftrightarrow q</math>).

It is also common to consider the ''always true'' formula and the ''always false'' formula to be connective (in which case they are [[nullary]]).
* [[Truth|True]] formula: <math>\top</math>, <math>1</math>, <math>V</math> (prefix), or <math>\mathrm{T}</math>;
* [[False (logic)|False]] formula: <math>\bot</math>, <math>0</math>, <math>O</math> (prefix), or <math>\mathrm{F}</math>.

This table summarizes the terminology:

{| class="wikitable" style="margin:1em auto; text-align:left;"
|-
! Connective 
! In English 
! Noun for parts 
! Verb phrase 
|-
! Conjunction 
| Both A and B 
| conjunct 
| A and B are conjoined
|-
! Disjunction 
| Either A or B, or both 
| disjunct 
| A and B are disjoined
|-
! Negation 
| It is not the case that A 
| negatum/negand 
| A is negated
|-
! Conditional 
| If A, then B 
| antecedent, consequent 
| B is implied by A
|-
! Biconditional 
| A if, and only if, B 
| equivalents
| A and B are equivalent
|}