Syllogism – Quick ‘n Awesome Tips You Need to Know

In Quants & Reasoning, Reasoning
March 19, 2016

Syllogism

Syllogism is an important topic in almost every competitive exam. In reality is a very easy scoring topic. But it is considered as a difficult topic for various reasons.
If you understand the below concepts, this will be the easiest topic. You don’t even need to revise it before exams.
You can solve the problems very easily in few seconds.

What is meant by Syllogism?

In simple words, syllogism is a form of reasoning in which a conclusion or conclusions are derived from the statements.
Our job is to find whether the given conclusion is correct or not. ie Follows or Not.
The given statements may not describe the real world scenario and they should be taken as they are and conclusions have to be drawn from the logic present in the statements.

Example

Statements

1. All Clouds are Phone
2. All Trains are Phone

Conclusions

I. All Clouds are Trains.
II. Some Clouds are Trains.

Answer

Neither I nor II follows.

How can we say this?

The correct conclusions can be drawn by following the logic in each of the given statements. This is easier for simple statements.
If complicated statements are given, the problem may lead to confusion.

Concepts of Syllogism

The concept of Syllogism can be understood with the help of some simple concepts using the Venn diagram method.
Don’t go to the next concept with out understanding the previous concept.
For your convenience, we have given one example problem for each Rule.

Different Concepts of Syllogism

Syllogism Concept Number One

Statement

Some A are B.

Venn Diagram

Possible Conclusions

1. Some A are B.
2. Some B are A.

Example

Statement

Some Apples are Oranges

Venn Diagram

Syllogism

Possible Conclusions

1. Some Apples are Oranges
2. Some Oranges are Apples

Syllogism Concept Number Two

Statement

All A are B.

Venn Diagram

Possible Conclusions

1. All A are B.
2. Some A are B.
3. Some B are A.

Example

Statements

All Apples are Oranges.

Venn Diagram

Possible Conclusions

1. All Apples are Oranges.
2. Some Apples are Oranges.
3. Some Oranges are Apples.

Syllogism Concept Number Three

Statement

No A is B

Venn Diagram

Possible Conclusions

1. No A is B.
2. No B is A.
3. Some A are not B.
4. Some B are not A.

Example

Statement

No Apple is Orange

Venn Diagram

Possible Conclusions

1. No Apple is Orange
2. No Orange is Apple
3. Some Apple is Not Orange
4. Some Orange is Not Apple

Syllogism Concept Number Four

Statements

1) Some A are B
2) Some B are A

Venn Diagram

Possible Conclusions

Between A and B:

1. Some A are B.
2. Some B are A.

Between B and C:

3. Some B are C.
4. Some C are B.

Between A and C

A and C are not directly connected to each other. So it is not possible to derive any kind of conclusion in normal situation. (Don’t bother about POSSIBILITY now. We will see that separately)

Example

Statements

1. Some Apples are Oranges
2. Some Oranges are Banana

Venn Diagram

Possible Conclusions

1. Some Apples are Oranges
2. Some Oranges are Apples

3. Some Oranges are Banana
4. Some Banana are Oranges

Apples & Banana cannot be related. No Direct relationship between these two.

Syllogism Concept Number Five

Statements

1. All A are B
2. All B are C

Venn Diagram

Possible Conclusions

Between A and B

1. All A are B
2. Some A are B
3. Some B are A

Between B and C

4. All B are C
5. Some B are C
6. Some C are B

Between A and C

7. All A are C
8. Some A are C
9. Some C are A

Example

Statements

1. All Apples are Oranges
2. All Oranges are Bananas

Venn Diagram

Possible Conclusions

1. All Apples are Oranges
2. Some Apples are Oranges
3. Some Oranges are Apples

4. All Oranges are Bananas
5. Some Oranges are Bananas
6. Some Bananas are Apples

7. All Apples are Bananas
8. Some Apples are Bananas
9. Some Bananas are Apples

Syllogism Concept Number Six

Statements

1. All A are B
2. All C are B

Venn Diagram

Possible Conclusions

Between A and B

1. All A are B
2. Some A are B
3. Some B are A

Between B and C

4. All C are B
5. Some C are B
6. Some B are C

Even though A and C are inside B, relation between A & C cannot be derived under normal condition as there is no direct connection.

Example

Statements

1. All Apples are Oranges
2. All Bananas are Oranges

Venn Diagram

Possible Conclusions

1. All Apples are Oranges
2. Some Apples are Oranges
3. Some Oranges are Apples

4. All Bananas are Oranges
5. Some Bananas are Oranges
6. Some Oranges are Bananas

Apples and Bananas cannot be related under normal conditions. Don’t confuse with Possibility Case Here. We will deal with that separately 🙂 🙂 🙂

Syllogism Concept Number Seven

Statements

1. No A is B.
2. No B is C.

Venn Diagram

Possible Conclusions

Between A and B

1. No A is B
2. No B is A

3. Some A are not B
4. Some B are not A

Between B and C

5. No B is C
6. No C is B

7. Some B are not C
8. Some C are not B

Example

Statements

1. No Apple is Orange
2. No Orange is Banana

Venn Diagram

Possible Conclusions

1. No Apple is Orange
2. No Orange is Apple
3. Some Apple is Not Orange
4. Some Orange is Not Apple

5. No Orange is Banana
6. No Banana is Orange
7. Some Orange is Not Banana
8. Some Banana is Not Orange

Syllogism Concept Number Eight (Some-All)

Statements

1. Some A are B
2. All B are C

Venn Diagram

Possible Conclusions

Between A and B

1. Some A are B
2. Some B are A

Between B and C

3. All B is C
4. Some B are C
5. Some C are B

Between A and C

6. Some A are C
7. Some C are A

Example

Statements

1. Some Apples are Oranges
2. All Oranges are Bananas

Venn Diagram

Possible Conclusions

1. Some Apples are Oranges
2. Some Oranges are Apples

3. All Oranges are Bananas
4. Some Oranges are Bananas
5. Some Bananas are Oranges

6. Some Apples are Bananas
7. Some Bananas are Apples

Here Relation between Apples and Bananas can be derived as there is direct connection between them.

Syllogism Concept Number Nine (All-Some)

Statements

1. All A are B.
2. Some B are C.

Venn Diagram

Possible Conclusions

Between A and B

1. All A is B
2. Some A are B
3. Some B are A

Between B and C

4. Some B are C.
5. Some C are B

Example

Statements

1. All Apples are Oranges

2. Some Oranges are Bananas

Venn Diagram

Possible Conclusions

1. All Apples are Oranges
2. Some Apples are Oranges

3. Some Oranges are Apples
4. Some Oranges are Bananas
5. Some Bananas are Oranges

Syllogism Concept Number Ten (All-Some)

Statements

1. All A are B.
2. Some A are C.

Venn Diagram

Possible Conclusions

Between A and B

1. All A are B
2. Some A are B
3. Some B are A

Between B and C

4. Some C are B
5. Some B are C

Between A and C

6. Some A are C
7. Some C are A

Example

Statements

1. All Apples are Oranges
2. Some Apples are Bananas

Venn Diagram

Possible Conclusions

1. All Apples are Oranges
2. Some Apples are Oranges
3. Some Oranges are Apples

4. Some Oranges are Bananas
5. Some Bananas are Apples

6. Some Apples are Bananas
7. Some Bananas are Apples

Syllogism Concept Number Eleven (Some-No)

Statements

1. Some A are B
2. No B is C

Venn Diagram

Possible Conclusions

Between A and B

1. Some A are B
2. Some B are A

Between B and C

3. No B is C
4. No C is B
5. Some B is not C
6. Some C is not B

Between A and C

7. Some A are not C

Points to Note

Now we have three different characters. ie A, B and C.
It is very clear that A and B are partners. Even though A doesn’t have any direct relationship with C, it can make SOME NOT relationship. ie Some A is not C.
Reverse is not possible. ie C can not make any relationship with A. (2 is greater than 1. Relationship can be derived where there are more Characters).

Example

Statements

1. Some Apples are Oranges
2. No Orange is Banana

Venn Diagram

Possible Conclusions

1. Some Apples are Oranges
2. Some Oranges are Apples

3. No Oranges is Banana
4. No Banana is Orange
5. Some Orange is Not Banana
6. Some Banana is Not Orange

7. Some Apples are Not Bananas

Syllogism Rule 12 (All-No)

Statements

1. All A are B
2. No B is C

Venn Diagram

Possible Conclusions

Between A and B:

1. All A are B.
2. Some A are B.
3. Some B are A.

Between B and C:

4. No B is C.
5. No C is B.
6. Some B are not C.
7. Some C are not B.

Between A and C:

8. No A is C.
9. No C is A.
10. Some A are not C.
11. Some C are not A.

Note

In this concept, A is inside B. Imagine B as a Mother & A is in the Womb. By Nature, whatever the Mother eats, that will pass to the Child as well. Similarly, whatever be the conclusion we can derive from B, the same type of conclusions can also be derived from A.

Example

Statements

1. All Apples are Oranges
2. No Orange is Banana

Venn Diagram

Possible Conclusions

1. All Apples are Oranges.
2. Some Apples are Oranges.
3. Some Oranges are Apples.

4. No Orange is Banana
5. No Banana is Orange.
6. Some Orange is not Banana
7. Some Banana is not Orange

8. No Apple is Banana
9. No Banana is Apple
10. Some Apple is not Banana
11. Some Banana is not Apple

Syllogism Concept Number Thirteen (All-No)

Statements

1. All A are B.
2. No A is C.

Venn Diagram

Possible Conclusions

Between A and B:

1. All A are B.
2. Some A are B.
3. Some B are A.

Between A and C:

4. No A is C.
5. No C is A.
6. Some A are not C.
7. Some C are not A.

Between B and C:

8. Some B are not C.

Note

In this Concept, A is inside B. A is directly connected with C. There is no direct connection between B and C. It is like feeding a baby in a Mother’s womb in some other way. As A and C are directly connected, the usual FOUR conclusions are possible. The only possible conclusion between B and C is Some B are not C. And the reverse is not possible.

Syllogism Rule Number Fourteen (Some-No)

Statements

1. Some A are B.
2. Some C are D.
3. No B is C.

Venn Diagram

Possible Conclusions

Between A and B

1. Some A are B.
2. Some B are A.

Between B and C

3. No B is C.
4. No C is B.
5. Some B is not C.
6. Some C is not B.

Between C and D

7. Some C are D.
8. Some D are C.

Between A and C

9. Some A are not C (While deriving conclusion between A and C, just forget D and simply follow Concept 11)

(Reverse is not possible)

Between B and D:

10. Some D are not B. (While deriving conclusion between B and D, just forget A and simply follow Concept 11)
(Reverse is not possible)

GOLDEN RULE OF SYLLOGISM

Only Positive Conclusions can be derived from Positive Statements. If all statements are positive, then all the conclusions must be positive.

Negative Conclusions can be derived from Negative Statements alone.

Merging Conditions

These conditions are used:

When two or more conclusions are FALSE.
If same characters are present in both statements.
If one conclusion is positive and the other is negative.

Example

POSITIVE	NEGATIVE
Some	No
All	Some not
Some	Some not

NOTE – All – No conditions cannot be merged.

Example

Statements

1. All pencils are grasshoppers
2. Some Grasshoppers are Clouds
3. Some Clouds are bottles

Conclusions
I. Some Bottles are Grasshoppers
II. Some Clouds are Pencils
III. No Pencil is Cloud.

Now we to check which of the given conclusions follow.

Venn Diagram

Conclusion I don’t follow – No Direct Connection Between Them.

Conclusion II don’t follow – No Direct Connection Between Them.

Conclusion III don’t follow – It is a Negative Conclusion (Golden Rule)

When more than Two Conclusions are false, you must Check the Merging Conditions.

Condition One – Is Two ore More Conclusions are False? – YES

Condition Two – Is it having Same Characters? – YES. Conclusion II and III are having same characters. ie Pencil and Cloud.

Condition Three – Are those conclusions are Positive and Negative? – YES. Conclusion II is Positive. Conclusion III is Negative.

Now the given Conclusions satisfy all the conditions. So It can be combined or merged.

The Answer is Either II are III Follows.

For Your Understanding, we have explained in detail. You can solve this in less than ten seconds.

Possibility

In simple words Possibility means capability of existing or happening. Don’t get confused while solving problems related to possibility. It is very simple. You just need to remember the below table.

GIVEN CONCLUSION	DESIRED CONCLUSION	POSSIBILITY
ALL	ALL	NOT POSSIBLE
SOME	SOME	NOT POSSIBLE
NO	NO	NOT POSSIBLE
NO	SOME NOT	NOT POSSIBLE
SOME	ALL	POSSIBLE
NO PROPER RELATION	SOME / ALL	POSSIBLE

– You can just remember the last two. Remaining things are NOT POSSIBLE.

Example 1

Statements

1. No Alia is Parineeti
2. Some Parineeti is Priyanka

Conclusions

1. No Alia is Priyanka
2. All Parineeti being Priyanka is a possibility

Always start with Venn Diagram

As per the above concept (Number 11) the only possible conclusion between Alia and Priyanka is Some Priyanka is not Alia. Here No Alia is Priyanks is given. So it is FALSE.

In Conclusion II, the existing relationship between Parineeti and Priyanka is SOME. The Desired relationship is ALL. So it is possible. (Refer the Table)

Answer is Conclusion II Follows.

Example 2

Statements

1. Some Sachin is Kohli
2. Some Raina is Kohli
3. Some Rayudu is Raina

Conclusions

1. Some Sachin is Raina
2. Some Rayudu being Kohli is a possibility
3. Atleast some Rayudu is Sachin
4. All Kohli being Raina is a possibility

Analysis of Conclusions

I – False – No Direct Relationship
II – No Direct Relation. It is Possibility Case. Desired in SOME. It Follows.
III – False – No Direct Relationship
IV – Possibility Case. Existing Relationship is Some. Desired is ALL. It Follows.

Answer II and IV Follows.