Parallel between logic and sets

In summary — Parallel logic ↔ sets

Propositional logic and the algebra of sets are the same object, written with two different notations:

Logic	Sets	Venn diagram
$\lnot p$	complement $\overline{A}$	outside of the circle
$p\land q$	intersection $A\cap B$	overlap
$p\lor q$	union $A\cup B$	sum of the circles
$p\veebar q$	symmetric difference $A\triangle B$	“crescent-shaped”
$p\Rightarrow q$	inclusion $A\subseteq B$	$A$ entirely inside $B$
$V$ (always true)	universe $U$	the whole rectangle
$F$ (always false)	empty set $\emptyset$	nothing

This dictionary is the key to reading the whole chapter: every logical property has a set-theoretic twin and vice versa.

Links

Topics: Set theory
Concepts: Logical connectives · Venn diagram
People: John Venn