Symmetric closure explained
on a
set
is the smallest
symmetric relation on
that contains
For example, if
is a set of airports and
means "there is a direct flight from airport
to airport
", then the symmetric closure of
is the relation "there is a direct flight either from
to
or from
to
". Or, if
is the set of humans and
is the relation 'parent of', then the symmetric closure of
is the relation "
is a parent or a child of
".
Definition
The symmetric closure
of a relation
on a set
is given by
In other words, the symmetric closure of
is the union of
with its
converse relation,
}.
References
