r.~r = relation that associates two atoms in the domain of
the relation r when they map to a common element
Transitive Closure
(/ Reachability)
Relation is transitive when contains tuples
a->b and b->c, it also contains a->c
^r = r + r.r + r.r.r...
child relation: a maps
each person to their child
Reflexive Transitive Closure
the smallest relation that contains r
and is both reflexive and transitive
is reflexive if its contains it's own
product for ever atom in itself
a->a
Domain and Range Restriction
s <: r contains tuples of a
relation r that start with an
element in set s
domain restriction of r to s
r :> s contains the tuples of r that
end with the element s
range restriction of r to s
Override
The override p++q of relation p by relation
q is like the union, except any tuple in p
that matches a tuple of q by starting with
same element is dropped.