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Syllogism concepts

Logical Reasoning(Banking) Syllogism

Syllogism concepts

Syllogism comes under the Verbal Reasoning Section and is a very important topic which is frequently asked in almost all the competitive exams. These types of questions are very simply framed. They contain generally two or more statements. These statements are then followed by a number of conclusions. Based on the statements, you have to find the authenticity of the conclusions. In simple words you have to find that from the given statements which conclusions logically follows them. The most widely used approach in solving these types of questions is the Venn diagram approach. There are various cases like certainity, possibility, reverse syllogs out of which questions are asked in exam. We will discuss each of them below.

CASE OF CERTAINITY

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 Between B and C

Some A is B Some B is C

Some B is A 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 Diagram is,

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:

Stmt : 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

Stmt : Some Cameras are Radios; Some Statues are Cameras.

Conclusion : Some Radios are statues; No Radio is a Statue.