5. Venn Diagrams
Some As are Not Some As are Bs
Bs
B
A
A A
B B
A
B A
B
A B
B
A
6. QUANTIFIERS
Basic
Premise Quantifier Subject Predicate
Quantifier
All Affirmative Universal
No Negative Universal
Some Affirmative Particular
Some Not Negative Particular
7. Rules
The middle term must not appear in
the conclusion
◦ All As are Bs Middle
◦ All Bs are Cs Term
◦ Conclusion cannot contain B
8. Rules
When both premises are
affirmative, conclusion cannot be
negative
All As are Bs
Some Bs are Cs
Then, conclusion should have only All
or Some as the quantifier.
9. Rules
There must be 3 and only 3 distinct
terms
When both premises are particular no
conclusion can be derived
◦ Some + some not, some + some, etc…
When both premises are negative, no
conclusion can be derived
◦ No + no, no + some not, some not + some
10. Rules
The middle term must be distributed at
least once.
◦ All As are Bs , Some Bs are Cs
◦ All As are Bs, Some As are Cs
11. Rules
If one of the premises is particular,
then conclusion is particular
Some Bs are Cs
All Cs are Ds
Conclusion has to have quantifier as
some.
12. Rules
When One Quantifier is negative, the
conclusion must be negative
No As are Bs
All Bs are Cs
Conclusion must have quantifier as
some not or No.
13. Rules
A term which isn’t distributed in the premise
should not be distributed in the conclusion.
All As are Bs
Middle
All Bs are Cs
Term
---------------------
All As are Cs
Some A/Cs are C/As
14. Lets Try an Example
You say that sappy movies are always
bad? I can prove that isn't true. For
instance, Steven Spielberg always
makes great movies! But some of his
movies are sappy. So, some sappy
movies are also great.
15. Solution
All Steven Speilberg movies are Great
Some Steven Speilberg movies are sappy
Answer is and
particular
Some Sappy movies are Great
