11 Basics and Rules in Syllogism Questions to Solve Quickly

syllogism-questions-rules

Basics and Rules in Syllogism Questions to Solve Quickly

Introduction to Syllogism Questions 

Syllogism basics and syllogism questions and answers

Syllogism Questions to Solve Quickly you need to understand the concept behind syllogism questions. Syllogism is a form of reasoning, in this we need to draw conclusions from the given assumed statements, maybe not real.

From the given statements we need to draw Venn diagram and from this diagram compare those given conclusions and conclude the given conclusion either followed or not to the Venn diagram.

If the conclusion is valid to the diagram, then it follows otherwise conclusion is invalid and not follows. This is the meaning of syllogism.

Basics of syllogism questions for easy understand

Here basic concepts are explained related to the  Syllogism Questions. Just here you need to understand relations between statements by drawing Venn diagrams and then conclude, the given conclusions are either invalid or invalid.
Note:
When there is “No” or “Some not”word present in the given statement, then that statement will be the negative statement.
If the word “No” or “Some not”absent in the statement, then that statement will be the positive statement.
It means either All or Some words present in the statement considered as positive statements.

Basic Concepts related to Positive Statements in Syllogism Questions

Basic Concept 1: Some A is B (Positive Statement)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 1The Venn diagram for the statement ” Some A is B
 By observing the diagram we can draw some
Possible Conclusions
 1. Some A is B. and also can be drawn another conclusion that is
 2. Some B is A.
 
Note: There is some attachment or relation (Green Marks) between A and B. So the attachment related to both A and B. So there are two conclusions are possible for this statement.

Basic Concept 2: All A is B ( Positive Statement)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 3

The Venn diagram for the statement “ All A is B
 By observing the diagram we can draw some
Possible Conclusions
1. All A is B. and also can be drawn other conclusions like
2. Some A is B.
3. Some B is A.
Note: In this statement, along with all A is in B, we can also observe that some part of A is in the B and some part of B related to A. So the other two conclusions like Some A is B and Some B is A is also possible.

Basic Concept 3: Some A is B; Some B is C ( Two Positive Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 5
The Venn diagram for the two statements.
Some A is B

Some B is C

Possible Conclusions are drawn between A and B
Some A is B
Some B is A
Possible Conclusions are drawn between B and C
Some B is C
Some C is B
Note:  In these two statements, the relation or attachment can be seen between A and B and between B and C only. There is no relation between A and C. So we can’t draw any conclusion between A and C.

 Basic Concept 4: All A is B; All B is C (Two Positive Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 7The Venn diagram for the two statements.
 “All A is B
 “All B is C
Possible Conclusions are drawn between A and B
All A is B     (Because of All A part present in the B)
Some A is B (Because of part of A is in the B)
Some B is A  (Because of some part of B is having relation with A)
Possible Conclusions are drawn between B and C
All B is C
Some B is C
Some C is B
 
Possible Conclusions are drawn between A and C
All A is C
Some A is C

Some C is A.

Basic Concept 4: Some A is B; All B is C. (Two Positive Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 9The Venn diagram for the two statements.
 “Some A is B
 “All B is C
Possible Conclusions are drawn between A and B
Some A is B (Because of some part of A is in the B)
Some B is A  (Because of some part of B is in the A)
Possible Conclusions are drawn between B and C
All B is C
Some B is C
Some C is B
 

Possible Conclusions are drawn between A and C
Some A is C
Some C is A

Basic Concept 5: All A is B;  Some B is C. (Two Positive Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 11The Venn diagram for the two statements.
 “All A is B

 “Some B is C

Possible Conclusions are drawn between A and B
All A is B (Because of  all part of A is in the B)
Some A is B (Because of  B is occupied by the A)
Some B is A  (Because of some part of B is occupied by the A)
Possible Conclusions are drawn B and C
Some B is C
Some C is B
 
Possible Conclusions are drawn between A and C
By observing the Venn diagram, there is no relation between A and C. So no conclusion drawn between A and C.

Basic Concept 6: All B is A; All C is A. (Two Positive Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 13
The Venn diagram for the two statements.
 “All B is A

 “All C is A

Possible Conclusions are drawn between A and B
All B is A (Because of  all part of B is in the A)
Some A is B (Some part of A is occupied by the B)
Some B is A  (Because of Some part of B is occupied by the A)
Possible Conclusions are drawn B and C
There is no relation or attachment between B and C. So we cannot be drawn any conclusion between B and C.
 
Possible Conclusions are drawn between A and C
All C is A
Some C is A
Some A is C

Basic Concepts related to Negative Statements (indicated with X )-Syllogism Questions

Basic Concept 1: No A is B. (Negative Statement)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 15 Venn diagrams possible for this negative statement.
  ” No A is B
Possible Conclusions are drawn between A and B
No A is B
No B is A
Some A is not B
Some B is not A
Note: In this case, some-not also can be drawn in conclusions

Basic Concept 2: All A is B; No B is C. ( Positive and Negative Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 17Venn diagram for this positive and negative statement.

 “All A is B” (Positive)
 “No B is C” (Negative)
Possible Conclusions are drawn between A and B
 All A is B
Some A is B
Some B is A
Possible Conclusions are drawn between B and C
No B is C (No direct relation between B and C)
No C is B
Some B is not C
Some C is not B
Possible Conclusions are drawn between A and C
No A is C
Some A is not C (No direct relation between A and C)

Basic Concept 3: All A is B;  No A is C. (Positive and Negative Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 19

Venn diagram for this positive and negative statement.

 “All A is B” (Positive)
 “No A is C” (Negative)

Possible Conclusions are drawn between A and B
All A is B
Some A is B
Some B is A
 
Possible Conclusions are drawn between B and C
Some B is not C
Note: In this case no direct indication of “x”  between B and C. So some-not only possible in conclusion.
Possible Conclusions are drawn between A and C
No A is C
Some A is not C (No direct relation between A and C)
No C is A
Some C is not A

Basic Concept 4: Some A is B; No B is C. (Positive and Negative Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 21

 

 

Venn diagram for this positive and negative statement.

Some A is B
No B is C
Possible Conclusions are drawn between A and B
 All A is B
Some B is A
 
Possible Conclusions are drawn between B and C
No B is C
No C is B
Some B is not C
Some C is not B
Possible Conclusions are drawn between A and C
Some A is not C
Note: In this case no direct indication of “x”  between A and C. So some-not only possible in conclusion.

Basic Concept 5: Some A is B; No A is C (Positive and Negative Statements)-Syllogism Questions

11 Basics and Rules in Syllogism Questions to Solve Quickly 23

 

 

 

Venn diagram for this positive and negative statement.

Some A is B
 No A is C
Possible Conclusions are drawn between A and B
Some A is B
Some B is A
 
Possible Conclusions are drawn between B and C
Some B is not C
Note: In this case no direct indication of “x”  between B and C. So some-not only possible in conclusion.
Possible Conclusions are drawn between A and C
No A is C
No C is A
Some A is not C
Some C is not A

Concepts related to Complementary Pairs (Given Conclusions not follows the Venn Diagram)

In this concept, one conclusion should be in positive ( All/ Some) and another conclusion should be in the negative (No or Some not). In this case, if individually both conclusions do not follow the diagram, then “Either or” will come to the final conclusion.

Syllogism Questions-Explanation of Syllogism in Complementary Pairs – ” Either or

Example for Complementary Pairs of Conclusions
(I) All A is B + Some A is not
(Here one conclusion is positive (All) and another one (Some not) is negative)
(II) Some A is B  + No A is B 
(Here one conclusion is positive (Some) and another one (No) is negative)
(III) Some A is B + Some A is not B
(Here one conclusion is positive (Some) and another one (Some not) is negative)
Example 1: 
Statements:
All Cows are Animals
No Dog is Cow.
Conclusions:
(I) No Dog is an Animal
(II) Some  Dogs are Animals.
Answer:

11 Basics and Rules in Syllogism Questions to Solve Quickly 25

 

Venn Diagram for given statements

According to conclusion 1:
No dog is an anima (Not followed diagram).
According to conclusion 2:
Some dogs are animals (Not followed diagram)
Both the given two conclusions are not followed Venn diagram, so they are false and satisfies the concept of complementary pairs. So the answer will be Either I or II follows.

Syllogism Questions-Concept-related to Possibility Case of Conclusions ( can be in conclusion )

In this concept, we need to draw two Venn diagrams.
1) Basic Diagram – According to given statements
2) Possibility Diagram – No given in statements, but may be possible to draw.

Here we need to compare “No” type of conclusion and “Possible” type of conclusion.

Note: Rules for Possibility Conclusions-Syllogism Questions

  • If the “No” type of conclusion is false in anyone diagram (Basic or Possibility), then ” No type of conclusion has not followed the diagram.
  • But here if “Possible” type of conclusion is true in anyone diagram (Basic or Possibility), then “Possible” type of conclusion has followed the diagram.
  • If “Possible” type of conclusion is true in both diagrams (Basic and Possibility), then “Possible” type of conclusion has followed the diagram.
  • If “Possible” type of conclusion is false in both diagrams (Basic and Possibility), then “Possible” type of conclusion has not followed the diagram.
11 Basics and Rules in Syllogism Questions to Solve Quickly 27
  • If all the parameters or statements in single Venn diagram, then “No” type of conclusion will be not followed.
    Example Venn diagram:

11 Basics and Rules in Syllogism Questions to Solve Quickly 29

Note: In this type Venn diagrams all parameters are considered in single Venn diagram only, so “No” type of conclusion not follows. But “ Possible ” type of conclusion must follow.
Explanation:
Example 1:
Statements
(I) Some Cars are Vehicles
(II) All Vehicles are Jeeps
(III) No Jeep is Truck

Venn Diagram 
(I) Basic 
11 Basics and Rules in Syllogism Questions to Solve Quickly 31
 
 
 
 
 
 
 
 
 
 
 



(II) Possibility Diagram – 1
11 Basics and Rules in Syllogism Questions to Solve Quickly 33
(III) Possibility Diagram -2 
11 Basics and Rules in Syllogism Questions to Solve Quickly 35
Note: While drawing the possible diagram, we can draw various possibility diagram, but we should not violate the given statements. Possible diagrams must match the statements.
Conclusions:
 
1. Some Trucks being cars is a possibility.
2. All Trucks being cars is a possibility.
According to rules for possible conclusions. If anyone diagram obeys the possibility conclusion, the possible conclusion must follow.
Conclusion 1
1. Some Trucks being cars is a possibility.
  • See the basic diagram above, there is no relation between trucks and cars. So the basic diagram not obeys the conclusion 1.
  • See the possible diagrams 1 and 2, there is a relation between cars and trucks. but no relation trucks and jeeps, hence we are not violating the statement of No Jeep is Truck. So the possible diagrams obey the conclusion1.
  • Finally, the conclusion 1 even not obeys by the basic diagram, the possible diagrams obeys. So the conclusion 1 must follow.
Conclusion 2
2. All Trucks being cars is a possibility.
  • See the basic diagram above, there is no relation between trucks and cars. So the basic diagram not obeys the conclusion 2.
  • See the possible diagrams 1, there is a relation between cars and trucks as All Trucks are Cars. but no relation trucks and jeeps, hence we are not violating the statement of No Jeep is Truck. So the possible diagrams obey the conclusion1.
  • Finally, the conclusion 2 even not obeys by the basic diagram, the possible diagram 2 obeys. So the conclusion 2 must follow.

Syllogism Questions-Some Examples of Possibility diagrams for Basic diagrams.

 
Statement: All Birds are Crows.
 
1. Basic Diagram

11 Basics and Rules in Syllogism Questions to Solve Quickly 37

Possible Diagram
11 Basics and Rules in Syllogism Questions to Solve Quickly 39
Statement: Some Birds are Crows.
 
1. Basic Diagram
11 Basics and Rules in Syllogism Questions to Solve Quickly 41
Possible Diagram
11 Basics and Rules in Syllogism Questions to Solve Quickly 43
Statement: Some Birds are not Crows.
 
1. Basic Diagram
11 Basics and Rules in Syllogism Questions to Solve Quickly 45
Possible Diagrams
 
11 Basics and Rules in Syllogism Questions to Solve Quickly 4711 Basics and Rules in Syllogism Questions to Solve Quickly 49
These are all entire concepts related to basics of syllogism. Practice more syllogism questions and answers for easy understanding and for more speed to draw conclusions.
Give you valuable feedback in the comment section. we will try our best to support your learning.

Related Articles

Responses

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

error: Content is protected !!