Zeroth order logic or propositional calculus.

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Zeroth order logic or propositional calculus.

This has its originals in Greece of the 4th century BC. Boole and de Morgan reformulated it in the nineteenth century as the study of boolean-valued variables.

Notation:

Symbol	Name
$\vee$	OR
$\wedge$	AND
$\neg$	NOT
$\Leftrightarrow$	Equivalent (same as =)
$\Rightarrow$	Implies

The last operator is defined by:

$p\Rightarrow q$ is true unless $p$ is true and $q$ is false

Basic facts:

Associativity

$(p\vee q)\vee r\Leftrightarrow p\vee (q\vee r)$

$(p\wedge q)\wedge r\Leftrightarrow p\wedge (q\wedge r)$

Distributivity

$p\wedge (q\vee r)\Leftrightarrow (p\wedge q)\vee (p\wedge r)$

$p\vee (q\wedge r)\Leftrightarrow (p\vee q)\wedge (p\vee r)$

De Morgan Laws

$\neg (p\wedge q)\Leftrightarrow \neg p\vee \neg q$

$\neg (p\vee q)\Leftrightarrow \neg p\vee \neg q$

Implication identity

$p\Rightarrow q\Leftrightarrow \neg p\vee q$

All of these identities can be proved via truth tables.

Justin R. Smith 2001-04-06