# Krzysztof Maurin's notation

## Analysis - Part I: Elements

[ilmath]\wedge[/ilmath] "and"
[ilmath]\bigwedge_x[/ilmath], $\bigwedge_x$ "for all [ilmath]x[/ilmath] there follows" Equiv to [ilmath]\forall x[/ilmath], [ilmath]x[/ilmath] may be a statement (eg: [ilmath]x:=y\in Y[/ilmath])
[ilmath]\vee[/ilmath] "or"
[ilmath]\bigvee_x[/ilmath], $\bigvee_x$ "there exists an [ilmath]x[/ilmath] such that" Equiv to [ilmath]\exists x[/ilmath], [ilmath]x[/ilmath] may be a statement (eg: [ilmath]x:=y\in Y[/ilmath])
[ilmath]¬[/ilmath] "Not"
[ilmath]\implies[/ilmath] "if, ..., then" Meaning: if left side then right side, see Implies
[ilmath]\iff[/ilmath] "if and only if" Implication in both directions, if left then right, if right then left
[ilmath]:=[/ilmath] "equal by definition"

## Examples

Maurin gives some examples:

• Contrapositive: [ilmath](p\implies q)\iff(¬q\implies ¬p)[/ilmath]
• De Morgan's laws: [ilmath]¬(p\wedge q)\iff(¬p\vee ¬q)[/ilmath] and [ilmath]¬(p\vee q)\iff(¬p\wedge ¬q)[/ilmath]

## References

1. Analysis - Part I: Elements - Krzysztof Maurin