<s>
The	O
above	O
concept	O
of	O
relation	O
has	O
been	O
generalized	O
to	O
admit	O
relations	O
between	O
members	O
of	O
two	O
different	O
sets	O
(	O
heterogeneous	O
relation	O
,	O
like	O
"	O
lies	O
on	O
"	O
between	O
the	O
set	O
of	O
all	O
points	O
and	O
that	O
of	O
all	O
lines	O
in	O
geometry	O
)	O
,	O
relations	O
between	O
three	O
or	O
more	O
sets	O
(	O
Finitary	B-Algorithm
relation	I-Algorithm
,	O
like	O
"	O
person	O
x	O
lives	O
in	O
town	O
y	O
at	O
time	O
z	O
"	O
)	O
,	O
and	O
relations	O
between	O
classes	O
(	O
like	O
"	O
is	O
an	O
element	O
of	O
"	O
on	O
the	O
class	O
of	O
all	O
sets	O
,	O
see	O
)	O
.	O
</s>
<s>
The	O
representation	O
of	O
Rdiv	O
as	O
a	O
boolean	B-Algorithm
matrix	I-Algorithm
is	O
shown	O
in	O
the	O
left	O
table	O
;	O
the	O
representation	O
both	O
as	O
a	O
Hasse	O
diagram	O
and	O
as	O
a	O
directed	O
graph	O
is	O
shown	O
in	O
the	O
right	O
picture	O
.	O
</s>
<s>
In	O
the	O
boolean	B-Algorithm
matrix	I-Algorithm
representing	O
Rdiv	O
,	O
the	O
element	O
in	O
line	O
x	O
,	O
column	O
y	O
is	O
""	O
.	O
</s>
<s>
Such	O
a	O
relation	O
is	O
called	O
a	O
multivalued	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
Surjective	B-Algorithm
(	O
also	O
called	O
right-total	O
or	O
onto	O
)	O
For	O
all	O
y	O
in	O
X	O
,	O
there	O
exists	O
an	O
x	O
in	O
X	O
such	O
that	O
xRy	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
green	O
and	O
blue	O
binary	O
relations	O
in	O
the	O
diagram	O
are	O
surjective	B-Algorithm
,	O
but	O
the	O
red	O
one	O
is	O
not	O
(	O
as	O
it	O
does	O
not	O
relate	O
any	O
real	O
number	O
to	O
−1	O
)	O
,	O
nor	O
is	O
the	O
black	O
one	O
(	O
as	O
it	O
does	O
not	O
relate	O
any	O
real	O
number	O
to	O
2	O
)	O
.	O
</s>
<s>
A	O
A	O
function	O
that	O
is	O
surjective	B-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
the	O
green	O
binary	O
relation	O
in	O
the	O
diagram	O
is	O
a	O
surjection	B-Algorithm
,	O
but	O
the	O
red	O
,	O
blue	O
and	O
black	O
ones	O
are	O
not	O
.	O
</s>
<s>
A	O
A	O
function	O
that	O
is	O
injective	O
and	O
surjective	B-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
the	O
green	O
binary	O
relation	O
in	O
the	O
diagram	O
is	O
a	O
bijection	B-Algorithm
,	O
but	O
the	O
red	O
,	O
blue	O
and	O
black	O
ones	O
are	O
not	O
.	O
</s>
