INTRODUCTION TO VENN DIAGRAMS
Introduction to Venn Diagrams
S
P
This is a Venn diagram for two terms. We can conceive of every element of S as being
within the boundary of the S circle. Everything which is not an S is found outside the
S circle.
Introduction to Venn Diagrams
S
P
This
In
a Venn
is a Venn
diagram,
diagram
we consider
for two terms.
the relationship
We can conceive
between
of two
everyterms,
element
or groups.
of S as being
We
overlapthe
within
each
boundary
circle toofmake
the Ssure
circle.
weEverything
consider every
which
logical
is notpossibility.
an S is found
Foroutside
any thing
thein
the
S
circle.
universe, it will be somewhere on this Venn diagram.
Introduction to Venn Diagrams
x
S
P
Inthe
If
a Venn
thing
diagram,
is neither
weinconsider
S nor in the
P, then
relationship
it is placed
between
outsidetwo
of both
terms,
circles.
or groups. We
overlap each circle to make sure we consider every logical possibility. For any thing in
the universe, it will be somewhere on this Venn diagram.
Introduction to Venn Diagrams
x
S
P
If the thing is neither in S nor in P, then it is placed outside of both circles.
If the thing is an S, but not a P, then it would go in the left crescent-shaped region.
Introduction to Venn Diagrams
x
S
P
If the thing is neither in S nor in P, then it is placed outside of both circles.
If the thing is an S, but not a P, then it would go in the left crescent-shaped region.
If it is a P, but not an S, then it goes in the right crescent-shaped region.
Introduction to Venn Diagrams
x
S
P
If the thing is neither in S nor in P, then it is placed outside of both circles.
If the thing is an S, but not a P, then it would go in the left crescent-shaped region.
If it is a P, but not an S, then it goes in the right crescent-shaped region.
Finally, the center “football” region is reserved for things which are both S and P.
Introduction to Venn Diagrams
x
S
P
If the thing is neither in S nor in P, then it is placed outside of both circles.
If the thing is an S, but not a P, then it would go in the left crescent-shaped region.
If it is a P, but not an S, then it goes in the right crescent-shaped region.
Finally, the center “football” region is reserved for things which are both S and P.
Introduction to Venn Diagrams
S
P
In a categorical statement we are saying something about the S circle, specifically
whether any region is empty or else has something in it. It can’t be both, but we
might not know which one it is. When we leave an area blank, that just means that
we don’t know whether there is an element in it, or else is empty.
Introduction to Venn Diagrams
S
P
In the
a categorical
Venn diagram
statement
above,we
everything
are sayingissomething
blank. This about
meansthe
that
S circle,
I don’tspecifically
have any
whether anyabout
information
regionthe
is empty
relationship
or elsebetween
has something
S and P.inItit.does
It can’t
not be
mean
both,
that
butthe
weareas
might
are
empty.
not know
A blank
which
space
onesimply
it is. When
means
wethat
leave
myan
information
area blank,orthat
knowledge
just means
about
that
we don’t
the
givenknow
area iswhether
“empty”.
there
Theisarea
an element
could beinempty,
it, or else
or itiscould
empty.
have something in it.
Introduction to Venn Diagrams
1
S
2
3
P
In the we
Since
Venn
arediagram
saying something
above, everything
about the
is blank.
subject
This
term,
means
we will
thatconcentrate
I don’t haveon
any
the S
circle. The Sabout
information
circle has
the two
relationship
regions,between
one which
S and
is outside
P. It does
of P,not
andmean
one which
that the
is inside
areas
of P.empty.
are
We canAsay
blank
about
space
a region
simplythat
means
it is either
that my
empty,
information
or that or
it has
knowledge
something
about
in it.
So, that
the
givengives
areaus
is “empty”.
a total of four
The area
things
could
we can
be empty,
say. Let’s
or number
it could have
each something
region.
in it.
Introduction to Venn Diagrams
1
S
2
3
P
Since
We
can
wesay
areabout
saying
region
something
one either
about
that
theitsubject
is empty,
term,
or that
we will
it has
concentrate
somethingon
in the
it. To
S
say that
circle.
The
it isSempty,
circle has
wetwo
shade
regions,
in theone
entire
which
region.
is outside
Click the
of P,mouse
and one
to fill
which
in area
is inside
1.
Click
of
P. We
again
cantosay
seeabout
whataitregion
looks like
thattoit say
is either
that region
empty,1or
is that
not empty.
it has something in it.
So, that gives us a total of four things we can say. Let’s number each region.
Introduction to Venn Diagrams
1
2
3
x
S
P
We can say about region one either that it is empty, or that it has something in it. To
say that it is empty, we shade in the entire region. Click the mouse to fill in area 1.
Click again to see what it looks like to say that region 1 is not empty.
Introduction to Venn Diagrams
1
x
S
2
3
x
P
To show
We
can say
that
about
area region
two is empty,
one either
we that
can shade
it is empty,
it. Click
or that
the mouse
it has something
to show that
in it.
area
To
say
2
is empty.
that it isClick
empty,
thewe
mouse
shade
again
in the
toentire
show region.
that areaClick
2 is the
not mouse
empty.to fill in area 1.
Click again to see what it looks like to say that region 1 is not empty.
Introduction to Venn Diagrams
1
2
3
x
S
P
So,show
To
therethat
are four
area things
two is we
empty,
can say
we can
about
shade
S in it.
comparison
Click the mouse
to P. We
tocan
show
saythat
thatarea
the
2 is empty.
area
of S outside
Click the
of Pmouse
is empty,
again
or that
to show
it has
that
something
area 2 is in
not
it.empty.
We could also say that
the area of S inside of P is either empty or has something in it. Each one of these
statements has a simple English counterpart, which we will see in the next slide.
Introduction to Venn Diagrams
1
2
S
“Area 1 is empty” corresponds to
“Area 2 is empty” corresponds to
“Area 2 has at least one element” corresponds to
“Area 1 has at least one element” corresponds to
3
P
Click the statements
to see the Venn
diagram for each.
Click here to move on.
Introduction to Venn Diagrams
1
2
S
“Area 1 is empty” corresponds to
“Area 2 is empty” corresponds to
“Area 2 has at least one element” corresponds to
“Area 1 has at least one element” corresponds to
3
P
Click the statements
to see the Venn
diagram for each.
Click here to move on.
Introduction to Venn Diagrams
1
2
S
“Area 1 is empty” corresponds to
“Area 2 is empty” corresponds to
“Area 2 has at least one element” corresponds to
“Area 1 has at least one element” corresponds to
3
P
Click the statements
to see the Venn
diagram for each.
Click here to move on.
Introduction to Venn Diagrams
1
2
3
x
S
“Area 1 is empty” corresponds to
“Area 2 is empty” corresponds to
“Area 2 has at least one element” corresponds to
“Area 1 has at least one element” corresponds to
P
Click the statements
to see the Venn
diagram for each.
Click here to move on.
Introduction to Venn Diagrams
1
2
3
x
S
“Area 1 is empty” corresponds to
“Area 2 is empty” corresponds to
“Area 2 has at least one element” corresponds to
“Area 1 has at least one element” corresponds to
P
Click the statements
to see the Venn
diagram for each.
Click here to move on.
Introduction to Venn Diagrams
1
2
S
“Area 1 is empty” corresponds to
“Area 2 is empty” corresponds to
“Area 2 has at least one element” corresponds to
“Area 1 has at least one element” corresponds to
3
P
Click the statements
to see the Venn
diagram for each.
Click here to move on.
Introduction to Venn Diagrams
1
S
2
3
P
Congratulations! You have now been introduced to Venn diagrams for categorical
statements. Hopefully you will find them useful.