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podzbiorem

Podzbiorem is the instrumental form of the Polish term podzbiór, used in mathematics to refer to the concept of a subset. In set theory, a set A is a subset of a set B if every element of A is also an element of B. Notation: A ⊆ B denotes a (not necessarily proper) subset, while A ⊂ B is commonly used to indicate a proper subset, where A ≠ B. The empty set ∅ is a subset of every set, and every set is a subset of itself (reflexivity).

Examples help illustrate the idea. Let A = {1, 3, 5} and B = {1, 2, 3, 4, 5}.

Subsets support basic operations. If A and B are subsets of a universal set U, then A

In Polish mathematical usage, podzbiór (and its instrumental form podzbiorem) is used similarly to denote a

Then
A
⊆
B,
and
A
⊂
B
because
B
contains
elements
not
in
A.
The
power
set
P(S)
is
the
set
of
all
subsets
of
S;
if
|S|
=
n,
then
|P(S)|
=
2^n.
Subset
relations
are
transitive:
if
A
⊆
B
and
B
⊆
C,
then
A
⊆
C.
∩
B
and
A
∪
B
are
also
subsets
of
U.
The
complement
of
A
with
respect
to
U,
written
U
\
A,
is
another
subset
of
U.
Subsets
underpin
many
mathematical
constructions,
including
functions
(as
sets
of
ordered
pairs),
logic,
and
combinatorics.
subset
of
a
given
set.
The
term
is
fundamental
to
set
theory
and
underlies
definitions
of
membership,
equality
of
sets,
and
cardinality.