�

�

�

�

�

�

(Premise) (Conclusion)

(John Venn)

S P

S P

S P

S P

(Quantifiers)

‘S’ ‘P’

(Subject)

(Copula)

�

�

(Total class inclusion relation)

(Total class exclusion relation)

(Universal Affirmative)

(Universal Negative) (Particular Affirmative)

(Particular Negative) A, E, I

S P S P

S P

S P

S P’

A, E, I O

S P

‘A’

S P

‘E’

‘E’

S P

‘I’

‘I’

S P

‘O’

‘A’

‘B’

‘I’

‘O’

(Category)

(Class)

(Some)

‘A’

‘E’

(Iconic representations of categorical proposition and

arguments to display their logical forms using overlapping circles.)

(Elementary Set Theory)

�

�

�

�

“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

‘‘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’

(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

‘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

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

(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

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

O: S P

S P

X

�

�

� 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)

A, E, I O

Λ � S P = SP = O

E: S P

SP = O

A, E, I O

*** ***** ***