Syllogism is one of the most important and interesting topics in
Reasoning and Solving Syllogism is always fun if you understand the
shortcuts. If you understand the below concepts I assure you that you
can solve 5 Syllogism problems in just 2 mins. Yes. Just 2 mins.
Have a Pen with you. Go through all the concepts one by one.
Understand how to draw Venn Diagrams for each concepts. Then understand
how the conclusion are made for each concepts.(Just don’t Scroll down
fast!!!).
Then work out the problems.
I insist you again. GO ONE BY ONE. Understand it. Then go to the next
one. Make sure you are thorough enough with the given concepts.
You don’t need to memorize any statements or any conclusions. All you need is to UNDERSTAND.
The first step is to make a Venn diagram. Second step is deriving the
conclusion. Let’s go to all possible concepts. (Concepts = Statements)
CONCEPT 1 Some A is B.
The Diagram for Some A is B is
The possible conclusions are,
1) Some A is B
2) Some B is A
CONCEPT – 2 – Some A is B and Some B is C
The Diagram is,
Now the Possible Conclusions are,
Between A and B Some A is B Some B is A
Between B and C Some B is C Some C is B
There is no DIRECT CONNECTION between A and C. So it is not possible to derive any conclusion between A and C.
CONCEPT 3 – All A is B
The Conclusions are,
All A is B.
Some A is B.
Some B is A.
IMPORTANT NOTE : WHEN THE STATEMENTS ARE POSITIVE, THE CONCLUSIONS MUST BE POSITIVE.
CONCEPT 4 – All A is B and All B is C
The Conclusions are,
Between A and B Between B and C Between A and C
All A is B. All B is C. All A is C.
Some A is B. Some B is C. Some A is C.
Some B is A. Some C is B. Some C is A.
Concept 5 – Some A is B. All B is C.
The possible conclusions are,
Between A and B Between B and C Between A and C
Some A is B All B is C Some A is C
Some B is A Some B is C Some C is A
Some C is B
Concept 6 – All A is B and Some B is C
The possible conclusions are,
Between A and B Between B and C
All A is B Some B is C
Some A is B Some C is B
Some B is A
There is no DIRECT CONNECTION between A and C. So it is not possible to derive any conclusion between A and C.
Concept 7 – All B is A and All C is A
The Possible Conclusions are,
Between A and B Between A and C
All B is A All C is A
Some B is A Some C is A
Some A is B Some A is C
There is no DIRECT CONNECTION between B and C. So it is not possible to derive any conclusion between B and C.
Concept 8 – No A is B
The Possible Conclusions are,
No A is B
No B is A
Some A is not B
Some B is not A
When NO comes in Statement, Some-not should follow in Conclusion
Concept 9 – All A is B and No B is C
The Possible Conclusions are,
Between A and B Between B and C Between A and C
All A is B No B is C No A is C
Some A is B No C is B Some A is Not C
Some B is A Some B is not C
Some C is not B
Concept 10 – All A is B and No A is C
The Possible Conclusions are,
Between A and B Between A and C Between B and C
All A is B No A is C Some B is not C
Some A is B No C is A
Some B is A Some A is not C
Some C is not A
Concept 11 – Some A is B; No B is C
The Possible Conclusions are,
Between A and B Between B and C Between A and C
Some A is B No B is C Some A is not C
Some B is A No C is B
————————————Some B is not C
————————————Some C is not B
Concept 12 – Some A is B; No A is C
The Possible Conclusions are,
Between A and B Between A and C Between B and C
Some A is B No A is C Some B is not C
Some B is A No C is A
——————————— Some A is not C
——————————— Some C is not A
Note: In all the above, the conclusions are made based on the statements. There in only one case where the conclusions are determined based on the conclusion itself. It is called as Merging Concept.
MERGING CONCEPT
This concept is applicable when more than one conclusion does not follows.
Rules:
- The two non-following conclusions must be of same character.
- One conclusion must be positive (All/Some)
- One conclusion must be negative (No/Some-not)
- Let me explain this concept with some examples.
Example 1:
Statement : All Lotus are Flowers; No Lilly is Lotus.
Conclusion: No Lilly is a flower; Some Lilly is Flowers.
The first step is to draw Venn Diagram.
Now Check the conclusions.
No Lilly is a flower. (It’s not true)
Some Lilly is flowers (It is also not true)
Two conclusions are false. And Both are same Characters (Lilly and
Flower). One is Positive and one is negative. It satisfies all the rules
of Merging Concept.
So the Answer is Either (i) or (ii) Follows.
Example 2
Statement : Some Cameras are Radios; Some Statues are Cameras.
Conclusion : Some Radios are statues; No Radio is a Statue.
Conclusion 1 : Some Statues are Radios (It is false) (No direct relation between Statue and Radio)
Conclusion 2: No Radio is a Statue (It is False) (It is a negative
conclusion) (When statements are positive,
conclusions must be positive).
Now Check for merging concept.
Two Conclusions are False.
They are of same character. One is Positive and other is Negative.
Answer is Either (I) or (II) Follows
POSSIBILITY
Whenever the term “Possibility” OR “Can” comes in Conclusion, We need to check this simple table.
Let me explain you guys with an example.
Statements:
Some Mangoes are Apples; Some Bananas are Apples; Some Branches are Bananas
Conclusions:
Some Mangoes are Bananas
Some Branches Being Apples is a Possibility
Some Branches are Mangoes
All Apples Being Mangoes is a Possibility
The First Step is to draw Diagram.
Conclusion 1 : It is False. (No Direct Connection between them).
Conclusion 2: No relation between Branches and Apples. “Possibility” is there. (Chk Table) (It is True)
Conclusion 3: It is False (No Direct relation)
Conclusion 4: Between Apples and Mangoes “Some” can come. “Possibility is there” (Check Table). It is also true.
So the conclusion is II and IV Follows.