Figure
3.12.1:
The
general
inclusionexclusion
principle
applied
to
four
sets.
AUBUCUD
=
A+B+C
+
D
—ANnB]ANC—ANnD—BNC—BND—CnND)
+ANBNC+ANBND+ANCND+BNCND
—AnBNCND
:':;,T",fT':AT'ON
3.12.6:
Applying
the
general
inclusionexclusion
principle.
reeapnack:s
(add
the
sizes
of
the
sets)
(subtract
pairwise
intersections)
(add
threeway
intersections)
(subtract
the
fourway
intersectio
Feedback?
1)
Suppose
you
are
using
the
inclusionexclusion
principle
to
compute
the
number
of
elements
in
the
union
of
four
sets.
Each
set
has
15
Comract
elements.
The
pairwise
intersections
have
5
elements
each.
The
37
threeway
intersections
have
2
elements
each.
There
is
only
one
element
in
the
intersection
of
all
four
sets.
What
is
the
size
of
the
There
are
(;1)
pairwise
intersections,
each
of
which
has
5
union?
elements.
There
are
(g)
threeway
intersections,
each
of
37
which
has
2
elements.
There
is
only
one
intersection
of
z
all
four
sets.
eck
Sh
ow
answer
4.15_('21)54(§)2—1=60—65+4'2—1=37
CHALLENGE
.
:
:


ACTIVITY
3.12.1:
The
general
inclusionexclusion
principle.
Jump
to
level
1
Given
two
sets:
A
and
B.
A
has
5
elements.
B
has
9.
A
and
B
share
3
elements.
How
many
elements
are
there
in
total?
Feedback?
B
~J~0