2. Meaning of Syllogism
• A word given by the Greeks which means 'Inference' or
'Deduction'. We get to deduce logically from the given
propositions. Each proposition has a subject and a
predicate and we get to establish the relationship
between them.
• Propositions : Sentence that makes a relation between
subject and predicate.
3. Solving Syllogism by Venn Diagram
• Diagrams are pictorial ways of representing interactions
among sets to display information that can be read
easily.
• Syllogisms can be solved in many ways, however the
most frequently used method is by using the so called
“Venn diagrams”.
• Venn diagram show all possible and hypothetically
logical relations between a collection of finite and infinite
statements.
4. Type of propositions
Type of propositions Universal Particular
Positive A Format
All S are P
I Format
Some S are P
Negative E Format
No S are P
O Format
Some S are not P
5. Mediate and Immediate Inferences
Syllogism is actually a problem of mediate inferences.
For Example:
Statement: All S are P
All P are Q.
Inference: All S are Q.
While in Immediate Inference conclusion are drawn from only one
given proposition.
Statement: All Coasts are Beaches.
Immediate Inference: Some Beaches are Coasts.
6. Immediate Inference
Statement : All S are P.
P
S
Sl.No Conclusions
I No S are P
II Some S are P
III Some S are not
P
IV All P are S
V No P are S
VI Some P are S
VII Some P are not
S
Venn-Diagram
method is based on
Minimum
Overlapping
Concept.
Remarks
X
√
X
---
X
√
---
7. Immedite Inference• Statement : NO S are P.
Sl.No Conclusions
I All S are P
II Some S are P
III Some S are not
P
IV All P are S
V No P are S
VI Some P are S
VII Some P are not
S
Venn-Diagram
method is based on
Minimum
Overlapping
Concept.
Remarks
X
X
√
X
√
X
√
PS
VIII Only Some S are not P :
Not follows
8. PS
Immediate Inference
Statement: Some S are P.
Sl.No Conclusions
I All S are P
II No S are P
III Some S are not
P
IV All P are S
V No P are S
VI Some P are S
VII Some P are not
S
Venn-Diagram
method is based on
Minimum
Overlapping
Concept.
Remarks
---
X
---
---
X
√
---
9. Statement : Some S are not P.
Sl.No Conclusions
I All S are P
II No S are P
III Some S are P
IV All P are S
V No P are S
VI Some P are S
VII Some P are not
S
Venn-Diagram
method is based on
Minimum
Overlapping
Concept.
Remarks
X
---
---
---
---
---
---
S P
10. Immediate Inference
• Illustration:
• Statement: Some B are C.
• 1. Conclusions: I. All B are C.
• II. Some B are not C.
• 2. Conclusions: I. All B are C.
• II. Some C are not B.
Thumb Rule for Either or Conclusions:
Rule-1. I. ----- II. -----
Rule-2. I. +ive II. –ive
Rule-3. I. S P
II. S P
Rule-4. All, No can’t be either or.
11. Mediate Inferences
"All" Type Propositions
Statement:
• All students in my batch are Intellegent
• Ram belongs to my batch
Conclusion:
• Ram is Intellegent
12. Mediate Inferences
"All & No" Type Propositions
Statement:
• All students in my batch are Intellegent
• Sham does not belong to my batch
Conclusion:
• Sham is not Intellegent
• Sham is Intellegent
13. Mediate Inferences
"All & Some Not" Type Propositions
Statement:
• All students in my batch are Intellegent
• Some students in this batch are topper
Conclusion:
• Some toppers in this bach are Intellegent
• Some toppers are not Intellegent
• All toppers are Intellegent
14. Mediate Inferences
"All & Some Not" Type Propositions
Statement:
• All students in my batch are Intellegent
• Some students are not toppers
Conclusion:
• Some Intellegent are topper
• Some Intellegent are not topper
• Some students are topper
• Some students are not topper
15. Tips to confirm Conclusions
1.Draw a BD and confirm the given conclusions by visualizing the ADs.
2. If any conclusion being a possibility case, its not a necessary
condition, as atleast one possibility can confirm the conclusion.
Other than this, any conclusion (either in +ve or -ve tone, should be
treated as necessary condition.
3. If the middle term is missing in the two cosequetive statements, one
statement should be skipped to find the link in the other statement.
The skipped statement can be caught up later to complete the basic
minimum diagram.
4. If the Subjects and Predicates of the two given conclusions are same
and they are contradictory in nature i.e. one in +ve and other in -ve
in nature, it's the case of either/or. Apply the thumb rule.
