Venn Diagrams

1
Venn Diagrams
1 s that are not p 2 s that are p 3 p that
are not s
2
3
1
S
P
2
Universal Propositions
S
P
S
P
No S are P
All S are P
3
Particular Propositions

• Some S are P

• Some S are not P

X
X
P
S
P
S
4
Syllogism Diagrams
S Smokers P Philosophers
P
S
M Musicians
1 Smokers that are not
Philosophers or Musicians
3
2
1
2 Non-Musician Philosophers
who smoke.
5
3 Non-Musician Philosophers
4
6
who dont smoke
4 Musicians who smoke and
7
who are not Philosophers
5 Musician Philosophers who
smoke
M
6 Musician Philosophers who
dont smoke.
7 Non-smoking Musicians who arent Philosophers
5
The Venn Diagram Validity Test

• Diagram information from premises and inspect to
  see if the conclusion is implied if so, valid
  argument.
• 1. Enter marks (shading or x) only for
  premises, not for the conclusion.
• 2. Enter marks for universal premise first, if
  one is particular.

• 3. When entering information, focus on the two
  circles involved
• 4. The area where x goes is divided into two
  parts, if one part is shaded, put x in the
  other part if both parts are unshaded, put x
  on the line.

6
Venn Diagram, example 1

• No critical thinkers are cultists.
• All Applewhite followers are cultists.
• \ No Applewhite followers are critical thinkers.

A
T
Valid
C