# 11 Basics and Rules in Syllogism Questions to Solve Quickly

## Basics and Rules in Syllogism Questions to Solve Quickly

### Introduction to Syllogism QuestionsÂ

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

**Note:**

### Basic Concepts related to Positive Statements inÂ Syllogism Questions

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

**Â**By observing the diagram we can draw some

**Possible Conclusions**

**Â**

**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

**All A is B**“

**Â**By observing the diagram we can draw some

**Possible Conclusions**

**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

**Some A is B**“

“**Some B is C**”

**Possible ConclusionsÂ**

**are drawnÂ**

**between A and B**

**Possible ConclusionsÂ**

**are drawnÂ**

**between B and C**

**Note:Â**Â 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.

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

**All A is B**“

**All B is C**“

**Possible ConclusionsÂ**

**are drawnÂ**

**between A and B**

**Possible ConclusionsÂ**

**are drawnÂ**

**between B and C**

**Â**

**Possible ConclusionsÂ**

**are drawnÂ**

**between A and C**

Some C is A.

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

**Possible ConclusionsÂ**

**are drawnÂ**

**between A and B**

**Possible ConclusionsÂ**

**are drawnÂ**

**between B and C**

**Â**

**Possible ConclusionsÂ ****are drawnÂ ****between A and C**

Some A is C

Some C is A

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

**Possible Conclusions are drawn between A and B**

**Possible Conclusions are drawn B and C**

**Â**

**Possible Conclusions are drawn between A and C**

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

**Possible Conclusions are drawn between A and B**

**Possible Conclusions are drawn B and C**

**Â**

**Possible Conclusions are drawn between A and C**

### Basic Concepts related to Negative Statements (indicated withÂ XÂ )-Syllogism Questions

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

**No A is B**“

**Possible Conclusions are drawn between A and B**

**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

**All A is B**” (Positive)

**No B is C**” (Negative)

**Possible Conclusions are drawn between A and B**

**Possible Conclusions are drawn between B and C**

**Possible Conclusions are drawn between A and C**

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

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**

**Possible Conclusions are drawn between B and C**

**Note:**In this case no direct indication of “

**x**

**”Â**Â between B and C. So some-not only possible in conclusion.

**Possible Conclusions are drawn between A and C**

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

**Some A is B**“

**No B is C**“

**Possible Conclusions are drawn between A and B**

**Possible Conclusions are drawn between B and C**

**Possible Conclusions are drawn between A and C**

**Note:Â**In this case no direct indication of “

**x**

**”Â**Â 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

**Some A is B**“

**Â No A is C**“

**Possible Conclusions are drawn between A and B**

**Possible Conclusions are drawn between B and C**

**Note:Â**In this case no direct indication of “

**x**

**”Â**Â between B and C. So some-not only possible in conclusion.

**Possible Conclusions are drawn between A and C**

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

**Either or**” will come to the final conclusion.

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

**(I) All A is BÂ + Some A is not BÂ**

**(Here one conclusion is positive (All) and another one (Some not) is negative)**

**(II) Some A is BÂ Â + No A is BÂ**

**(Here one conclusion is positive (Some) and another one (No) is negative)**

**(III) Some A is BÂ + Some A is not B**

**(Here one conclusion is positive (Some) and another one (Some not) is negative)**

**Example 1:Â**

**Statements**:

**Conclusions:**

**Answer:**

**According to conclusion 1:**

**According to conclusion 2:**

**Either I or II follows**.

#### Syllogism Questions-Concept-related to Possibility Case of Conclusions ( *can be*Â 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.

- If all the parameters or statements in single Venn diagram, then “No” type of conclusion will be not followed.

**Example Venn diagram:**

**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:

Example 1:

**Statements**

**(I) Some Cars are Vehicles**

**(II) All Vehicles are Jeeps**

**(III) No Jeep is Truck**

Venn DiagramÂ

Venn DiagramÂ

**(I) BasicÂ**

**Â**

**Â**

**Â**

**Â**

**Â**

**Â**

**Â**

**Â**

**Â**

**Â**

**Â**

**(II) Possibility Diagram – 1**

**(III) Possibility Diagram -2Â**

**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:**

**Â**

**1. Some Trucks being cars is a possibility.**

**2. All Trucks being cars is a possibility.**

**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 asÂ
**All Trucks are Cars**. but no relation trucks and jeeps, hence we are not violating the statement ofÂ**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.**

**Â**

**Statement: All Birds are Crows.**

**Â**

**1. Basic Diagram**

**Possible Diagram**

**Statement: Some Birds are Crows.**

**Â**

**1. Basic Diagram**

**Possible Diagram**

**Statement:Â Some Birds are not Crows.**

**Â**

**1. Basic Diagram**

**Possible Diagrams**

**Â**

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