PPT: Syllogisms | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

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Syllogism
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Syllogism
What is Syllogism?
Definition
Syllogism is a logical reasoning method where a conclusion is drawn from two premises 
(statements) based on their relationships.
Structure
Major Premise + Minor Premise ³ Conclusion.
Example
Statements: 
All cats are dogs. 
All dogs are birds. 
Conclusion: All cats are birds.
Purpose
T ests your ability to analyze relationships and derive logical conclusions.
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Syllogism
What is Syllogism?
Definition
Syllogism is a logical reasoning method where a conclusion is drawn from two premises 
(statements) based on their relationships.
Structure
Major Premise + Minor Premise ³ Conclusion.
Example
Statements: 
All cats are dogs. 
All dogs are birds. 
Conclusion: All cats are birds.
Purpose
T ests your ability to analyze relationships and derive logical conclusions.
Types of Premises
Premise
A statement assumed true.
Universal Affirmative (All A are B)
Ex: All roses are flowers.
Universal Negative (No A is B)
Ex: No man is educated.
Particular Affirmative (Some A are 
B)
Ex: Some apples are fruits.
Particular Negative (Some A are 
not B)
Ex: Some scissors are not combs.
Special Case
"Only a few" ³ Small portion of A is B, not 
all.
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Syllogism
What is Syllogism?
Definition
Syllogism is a logical reasoning method where a conclusion is drawn from two premises 
(statements) based on their relationships.
Structure
Major Premise + Minor Premise ³ Conclusion.
Example
Statements: 
All cats are dogs. 
All dogs are birds. 
Conclusion: All cats are birds.
Purpose
T ests your ability to analyze relationships and derive logical conclusions.
Types of Premises
Premise
A statement assumed true.
Universal Affirmative (All A are B)
Ex: All roses are flowers.
Universal Negative (No A is B)
Ex: No man is educated.
Particular Affirmative (Some A are 
B)
Ex: Some apples are fruits.
Particular Negative (Some A are 
not B)
Ex: Some scissors are not combs.
Special Case
"Only a few" ³ Small portion of A is B, not 
all.
Patterns and Conclusions
Type 1: There are two statements provided followed by two conclusions numbered I and II. You 
have to take the two given statements as true even if they seem to be at variance with commonly 
known facts. Decide which conclusion logically follows from given statement.
Q: Statements: 
All roses are flowers. 
Some flowers are red.
Conclusion: 
I. Some roses are red. 
II. All red things are roses.
Select the correct conclusion(s): 
A) Only conclusion I 
B) Only conclusion II 
C) Both conclusions I and II 
D) Neither conclusion I nor II
Ans: A) Only conclusion I 
Explanation: Conclusion I is valid as it follows from the two statements (All roses are flowers, and 
some flowers are red). 
Conclusion II is not valid because we cannot infer that all red things are roses based on the given 
statements.
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Syllogism
What is Syllogism?
Definition
Syllogism is a logical reasoning method where a conclusion is drawn from two premises 
(statements) based on their relationships.
Structure
Major Premise + Minor Premise ³ Conclusion.
Example
Statements: 
All cats are dogs. 
All dogs are birds. 
Conclusion: All cats are birds.
Purpose
T ests your ability to analyze relationships and derive logical conclusions.
Types of Premises
Premise
A statement assumed true.
Universal Affirmative (All A are B)
Ex: All roses are flowers.
Universal Negative (No A is B)
Ex: No man is educated.
Particular Affirmative (Some A are 
B)
Ex: Some apples are fruits.
Particular Negative (Some A are 
not B)
Ex: Some scissors are not combs.
Special Case
"Only a few" ³ Small portion of A is B, not 
all.
Patterns and Conclusions
Type 1: There are two statements provided followed by two conclusions numbered I and II. You 
have to take the two given statements as true even if they seem to be at variance with commonly 
known facts. Decide which conclusion logically follows from given statement.
Q: Statements: 
All roses are flowers. 
Some flowers are red.
Conclusion: 
I. Some roses are red. 
II. All red things are roses.
Select the correct conclusion(s): 
A) Only conclusion I 
B) Only conclusion II 
C) Both conclusions I and II 
D) Neither conclusion I nor II
Ans: A) Only conclusion I 
Explanation: Conclusion I is valid as it follows from the two statements (All roses are flowers, and 
some flowers are red). 
Conclusion II is not valid because we cannot infer that all red things are roses based on the given 
statements.
Type 2
There are three statements provided followed 
by four conclusions numbered I,II, III, IV. You 
have to take the two given statements as true 
even if they seem to be at variance with 
commonly known facts. Decide which 
conclusion logically follows from given 
statement.
Select the correct conclusion(s): 
A) Only conclusion I and II 
B) Only conclusion II 
C) Only I and IV 
D) Only II and IV 
E) None
Q: Statements: 
(a) Some apples are fruits 
(b) All vegetables are fruits 
(c) All fruits are vegetables
Conclusions 
I. Some apples are vegetables 
II. All vegetables are fruits 
III. All fruits are apples 
IV . Alll vegetables are apples.
Ans: (a)
Sol: Combining (b) and (c), we have all 
vegetables are fruits (V ³ F) and all fruits are 
vegetables (F ³ V), implying vegetables and 
fruits are equivalent (V = F).
From (a), some apples are fruits, and since all 
fruits are vegetables (c), those apples are also 
vegetables, supporting I.
Conclusion II restates (b), so it9s true.
Conclusions III and IV require all fruits or all 
vegetables to be apples, which isn9t supported 
by <some apples are fruits. =
Result: Only conclusions I and II follow.
Answer: (A) Only conclusion I and II