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Propositional logic

A proposition is either true or false. With and, or, not and implication, propositions can be combined, and the truth value is decided with a truth table. An implication is false only when the premise is true and the conclusion false.

p \land q

and: true only when both are true

p \lor q

or: true when at least one is true

p \Rightarrow q \equiv \lnot p \lor q

implication

Symbols

$\lnot$	not
$\land$	and
$\lor$	or
$\Rightarrow$	if … then

Example

$p$ : it rains, $q$ : the ground is wet.

$p \Rightarrow q$ is false only if it rains and the ground is dry.

Anything follows from a false premise: then the implication is always true.

Practise logic and sets for free →

De Morgan's laws →

Part of Discrete Mathematics: Logic and sets.