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complementoA

ComplementoA is a notation used in some mathematical texts to denote the complement of a subset A within a universal set U. If A is a subset of U, the complementoA is the set of all elements in U that are not in A, often written as A^c or A'. The term complementoA appears in Portuguese- or Spanish-language writings as a descriptive label for the operation “take the complement of A in U.”

Definition and scope: The complement depends on the chosen universal set U. If U changes, the complementoA

Notation and properties: The complementoA operation is involutive: (A^c)^c = A. De Morgan’s laws relate complements to

Applications: In probability, if U is the sample space and P is a probability measure, P(A^c) = 1

Naming and usage: While complementoA is a descriptive label found in some publications, most texts prefer A^c

changes
accordingly.
For
example,
with
U
=
{1,
2,
3,
4,
5}
and
A
=
{2,
3},
the
complementoA
equals
{1,
4,
5}.
unions
and
intersections:
(A
∪
B)^c
=
A^c
∩
B^c
and
(A
∩
B)^c
=
A^c
∪
B^c.
A^c
is
sometimes
denoted
A′
or
Ac
in
various
texts.
−
P(A).
In
set
theory
and
logic,
the
complement
corresponds
to
negation
relative
to
U.
Venn
diagrams
commonly
illustrate
A
and
A^c
as
disjoint
regions
whose
union
covers
U.
or
A′
to
denote
the
complement
of
A.
The
term
reflects
the
broader
concept
of
taking
the
elements
not
belonging
to
a
given
subset
within
a
specified
universal
set.