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(Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

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Page 1: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

Page 2: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

(Premise) (Conclusion)

(John Venn)

Page 3: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

S P

S P

S P

S P

(Quantifiers)

‘S’ ‘P’

(Subject)

(Copula)

Page 4: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

(Total class inclusion relation)

(Total class exclusion relation)

(Universal Affirmative)

(Universal Negative) (Particular Affirmative)

(Particular Negative) A, E, I

Page 5: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

S P S P

S P

S P

S P’

A, E, I O

Page 6: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

S P

‘A’

S P

‘E’

‘E’

S P

‘I’

‘I’

S P

‘O’

‘A’

‘B’

‘I’

‘O’

(Category)

(Class)

(Some)

Page 7: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

‘A’

‘E’

Page 8: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

(Iconic representations of categorical proposition and

arguments to display their logical forms using overlapping circles.)

(Elementary Set Theory)

Page 9: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

“On the Diagrammatic

and Mechanical Representation of Propositions and Reasonings”

‘Philosophical

Magazine and Journal of Science’ (Venn-Diagram)

‘Eulerian Circles’

Venn-diagram

A Survey of Symbolic Logic

(Eulerian Circle)

(E) (A)

(A

(I

Page 10: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

‘‘The Mathematical Analysis of Logic’’ “An Investigation

of the Laws of Thought”

A– S

E– S

I– S P = S S P

O– S P = S S P

‘A’ ‘O’ ‘E’ ‘I’

A: SP– = 0 E: SP = 0

I = SP� 0 0 SP–� 0

‘I’ ‘O’

‘A’ ‘E’

‘A’ (T)

‘O’ (F) ‘I’

(F) ‘E’ (T)

‘A’ ‘O’

‘E’ ‘I’

‘E’ I

‘A’ ‘O’

Page 11: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

(Existential Import)

~, � , Λ, � �

Λ (Lamda) O (Zero)

‘S’- S’-

S = O

S’-

S � Λ S � O

‘S’

‘S’ S

S

(Product) (intersection)

SP S�P ‘‘S

P’’ (S Intersection P) ‘� ’

‘� ’ SP = S� P = =

SP � SP� O S� ~P = Λ

‘A’– S P = SP–

= O SP–

= Λ

Page 12: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

‘A’ ‘S’ ‘P’

‘E’– S P = SP = O SP = Λ

‘I’– S P = SP � O SP � Λ

‘I’

‘O’– S P = SP–� O SP

‘S’ P

‘S’

‘S’

‘X’

‘X’

‘S’

‘X’ ‘S’

S

S S

X

Page 13: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

A, E, I O

S

SP–

P– (P-bar) P

S–

P S– (S-bar)

S

SP

S

S–P–

S P

SP–

SP S–

P S–P–

S P

Page 14: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

(Universe of Discourse)

(Diagrams for Standard Form

Categorical Propositions)

‘A’

P

S P SP = O SP = Λ S

P S

‘A’

A: S P

SP– = O

E ‘E’

S P ‘S’

‘P’ SP = Λ SP = O

S ‘S’ P

‘E’

SP

Page 15: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

E: S P

SP = O

I ‘I’

S P S P

S P

‘S’ ‘P’ SP � O SP � Λ

S P ‘X’

‘I’

I: S P

SP � O

O ‘O’

S P ‘O’ S ‘S’ ‘P’

SP � O SP � S P

‘x’ ‘x

S, P ‘O’

S P

X

SP

Page 16: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

O: S P

S P

X

Page 17: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

� S P E-

S P S P O

S P

1) Baronett, S. and Sen, M.; Logic.

2) Chakraborti. C.; Logic-Informal, Symbolic & Inductive.

3) Copi, I. M. & Cohen, C.; Introduction to Logic.

4) Hurley, J. P.; Introduction to Logic.

5) Sharma. B. and Deka J.; A text Book of logic.

6) (https://www.lucidchart.com/blog/2013/01/17/a-history-of-the-venn-

diagram)

Page 18: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

A, E, I O

Λ � S P = SP = O

E: S P

SP = O

Page 19: (Premise) (Conclusion) (John Venn)...(Total class inclusion relation) (Total class exclusion relation) (Universal Affirmative) (Universal Negative) (Particular Affirmative) (Particular

A, E, I O

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