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complements

In mathematics and related fields, a complement is what remains when something is removed from a larger whole or what is needed to complete meaning. The notion appears in set theory, probability, logic, linguistics, and computer science, where a complement is often defined relative to a fixed universe or context.

In set theory, the complement of a subset A within a universal set U is the set

In probability, the complement of an event A is the event that A does not occur. If

In linguistics and grammar, a complement is a word, phrase, or clause that completes the meaning of

In logic and computer science, the complement often refers to negation or the NOT operation, which inverts

of
elements
in
U
that
are
not
in
A.
It
is
denoted
A^c
or
U\A.
Complementation
interacts
with
unions
and
intersections:
the
complement
of
a
union
equals
the
intersection
of
the
complements,
and
the
complement
of
an
intersection
equals
the
union
of
the
complements
(De
Morgan's
laws).
P(A)
is
the
probability
of
A,
then
P(A)
+
P(A^c)
=
1,
and
P(A^c)
=
1
−
P(A).
a
predicate
or
linking
verb.
For
example,
in
"She
believes
that
the
test
will
be
easy,"
the
clause
"that
the
test
will
be
easy"
is
a
complement;
in
"They
are
tired,"
"tired"
serves
as
a
predicative
complement.
a
truth
value
or
a
bit
pattern.
The
logical
complement
of
true
is
false,
and
the
bitwise
complement
flips
every
bit
in
a
binary
word.