Reasoning (Tricks To Solve Syllogism Questions Quickly 1 to 2)

Tricks To Solve Syllogism Questions Quickly

 

To solve the Syllogism section for IBPS Exam you need to know the following thing that includes all about syllogism as well as the tips and tricks to solve it.

What is Syllogism?

It is a kind of logical argument in which the conclusion is inferred form the premise. You will be given one preposition which is generally the conclusion and you have to infer from two or more such statements.

For example:

Premise 1: All men are fathers.

Premise 2: All fathers are caring.

Conclusion: All men are caring.

The standard way of solving a Syllogism is with the help of a Venn diagram. But in the exam you will not be able to draw a Venn diagram because of the time limit. To help you, here are some basic tips and tricks to solve the problems:

SHORTCUT RULES BETWEEN TWO STATEMENTS WHICH ARE IN THE ORDER:

• All + All = All
• All + No =No
• All + Some = No conclusion
• Some + All = Some
• Some + Some = No Conclusion
• Some + No = Some Not
• No + No = No Conclusion
• No + All = Some not reversed
• No + Some = Some not reversed

Cancel out the common terms in the given two statements and on the remaining terms, apply Syllogism rules and solve. The very first step is never assume. In syllogism a cat can either be a human or a dog can be a bird if the statement says so. All you have to do is to completely forget what you know and follow what the statement is saying.

REMEMBER SOME IMPLICATIONS:

• All <=> some, for example : All A are B also implies that some A are B and Some B are A
• Some <=> Some, for example: Some A are B also implies that some B are A
• No<=> No, for example :No A are B also implies that No B are A

Step 1: Classification of statements

Usually each statement has the following format:

“abc subject is/are (not) predicate.”

e.g.

All Cats Are Dogs.

Some Pigs Are not birds.

Based on the usage of “xyz” and “not”, the classification of the statements is as following

1. All cats are dogs: Universal Positive (UP)
2. Some dogs are birds: Particular Positive (PP)
3. No bird is a pig: Universal Negative        (UN)
4. Some pigs are not birds: Particular Negative (PN)

You have to remember the following words. You classify the statement accordingly whenever they are used:

• Universal (positive or negative): All, every, none, only, not a single, any etc.
• Particular (positive or negative): Some, many, a few, not many, most of, almost, generally, quite a few often, very little frequently, etc.

STEP 2: Standard Format – Conversation

Priority order: PP>UN>UP

Basically, a 2 premise Syllogism should the following basic form:

1. A—>B
2. B—>C

If in case it is not, then you should convert it to the above format.

NOTE:

• Question statements should have only three terms. Like A, B and C, as shown above.
• In the exam, if you encounter two question statements with four or more terms then you should be relieved! All you have to do is check the answer “no conclusion can be drawn”

E.g. if the statements are

1. All cats are birds
2. Some dogs are pigs

A–>B

C–>D

Here owing to four terms (cats, dogs, birds, and pigs) no conclusion can be drawn.

CONVERSION:

Now you have to learn how to convert the statements.

Universal Positive (UP)

Given Statement: All Cats are Dogs

The valid conversations can be:

• Some Cats are dogs (Particular Positive)
• Some dogs are cats (Particular Positive)

Hence, UP can be converted into PP.

Note: Only A is B –> All B are A

If the statement is “Only Birds are cats”, then better convert it into “All cats are Birds”.

Universal Negative (UN)

Given Statement: No Cats are pigs

Valid conversations can be:

• Some pigs are not cats (Particular Negative)
• No pigs are cats (Universal Negative)

Hence, UN can be converted to PN or UN.

Particular Positive (PP)

Given Statement: Some Cats are Dogs

Valid conversations can be:

Some dogs are cats (Particular Positive)

It means PP can be converted into PP only.

Particular Negative (PN)

In Particular negative statements, no conversion can be made.

Example: Some Cats are not Dogs

Hence,

• Universal Positive (UP): Only PP
• Universal Negative (UN): PN or UN
• Particular Positive (PP): Only PP
• Particular Negative (PN): Not possible.

 STEP 3: No Conclusion Combos

When two question statements are in following format, they are the non-conclusion combos:

• Universal Positive (UP), Particular Positive (PP), Particular Negative (PN)
• Universal Negative (UN), Universal Negative (UN), Particular Negative (PN)
• Particular Positive (PP), Particular Positive (PP), Particular Negative (PN)
• Particular Negative (PN), Any other (UP, UN, PP, PN)

For all the above combos, the answer would be no conclusion.

STEP 4: Conclusive Combos

Universal Positive (UP) + Universal Positive (UP) = Universal Positive (UP)

Universal Positive (UP) + Universal Negative (UN) = Universal Negative (UN)

Universal Negative (UN) + Universal positive (UP) = Particular Negative (PN)

Universal Negative (UN) + Particular Positive (PP) = Particular Negative

Particular Positive (PP) + Universal Positive (UP) = Particular Positive (PP)

Particular Positive (PP) + Universal Negative (UN) = Particular Negative (PN)

If we take the first statement from A to B and the Second statement from B to C, then the conclusion is usually in the format of A to C except when first statement is Universal Negative (UN).

 

BONUS TIPS FOR SIMPLIFYING SYLLOGISM PROBLEMS:

1. The First Tip to crack the Syllogisms is to NEVER ASSUME. A cat can be a human and a dog can be a bird if the statement says so then follow the statement even when you know both dogs and cats are animals. Forget what you know and follow the condition of the statement.
2. If a two related statement begins with All and followed by Some, it will conclude with Some
3. If a two related statement begins with Some, followed by All it will conclude with All
4. If two related statements begins with All and followed by No, it will end with NO
5. If two related statements begin with All and is followed by All, it will end with All
6. If two related statements begin with Some and is followed by Some the conclusion will in most cases be None
7. If No two statements are related the answer will be No Conclusion
8. Reverse also applies:
   
   • It means if the statement says All X is Y then it means that Some Y will also be X
   • If it says Some B is W it also means that Some W is B
   • If it says No Y is X then also means that No X is Y

 

Syllogism Concepts Part II

A statement has many conclusions (cases)

And thus, so many diagrams are possible!!

In possibility questions, the examiner asks if there exists any such case (diagram) where this conclusion is valid. So, you job is to find out this case. If there exists at least one such case, then the conclusion holds true. If not, then the conclusion is false. As simple as that!

Keeping this and also the previous Syllogism Post in mind, let’s solve some possibility questions.

Abbreviations that I used:

Basic Diagram = BD

Modified Diagram = MD

Question 1:

 Statements:

A. All flowers are trees

B. Some trees are houses

C. All houses are wheels

Let’s first make a BD according to these statements.

Conclusions:

1. At least some wheels are trees

2. Some trees are flowers

3. All wheels are flower is a possibility

Now, see the BD,

Conclusion 1 clearly follows. 

Conclusion 2 also clearly follows. 

But, what about Conclusion 3?

Let’s make a MD and see if it follows or not!

In the MD, we can clearly see that all the statements are still valid, and Conclusion 3 also is following. So, Conclusion 3 follows. 

• 1? Follows
• 2? Follows
• 3? Follows

Understood?

Let’s now solve another question!

Question 2:

Statements:

A. Some desks are chairs

B. Some chairs are pens

C. Some pens are drawers

First, make a BD according to these statements. 

Conclusions:

1. At least some drawers are desks

2. There is a possibility all drawers are chairs

3. No drawer is a chair

Now, see the BD

Conclusion 1 clearly doesn’t follow. 

But, what about Conclusion 2?

Let’s make a MD

See the MD, Conclusion 2 follows in it.

And if there is a possibility that All drawers are chairs, then how could No drawer is a chair follow?

So, Conclusion 3 will not follow! 

• 1? Doesn’t follows
• 2? Follows
• 3? Doesn’t follows

Understood?

Let’s solve another one!

Question 3:

Statements:

A. All politicians are corrupt

B. Some politicians are honest

C. No leader is honest

First, make a BD according to these statements.

Conclusions:

1. Some politicians are not leader

2. All honest being corrupt is a possibility

3. Some leaders are not corrupt

Now, see the BD, 

Some politicians, which are honest (Red Portion), cannot beleaders. 

So, Conclusion 1 clearly follows. 

But, what about Conclusion 2?

Let’s make a MD.

See the MD, Conclusion 2 clearly follows!

What about conclusion 3?

Let’s make another MD.

See the last diagram, All leaders are corrupt could be a possibility! So, Conclusion 3 doesn’t follow. 

• 1? Follows
• 2? Follows
• 3? Doesn’t follows

Understood?

Question 4:

Statements:

A. Some people are intelligent

B. All intelligent are honest

C. No intelligent is smart

First, make a BD according to these statements.

Conclusions:

1. Some honest are not smart

2. All people being honest is a possibility

3. Some honest are people

Now, see the BD, 

Some honest, which are intelligent (Red Portion), cannot be smart. 

So, Conclusion 1 follows.

But, what about Conclusion 2?

Let’s make a MD.

See the MD, Conclusion 2 clearly follows.

Conclusion 3 also follows. 

• 1? Follows
• 2? Follows
• 3? Follows

Understood?

Question 5:

Statements:

A. Some writers are poets

B. All poets are singers

C. Many singers are actors

D. No singer is a dancer

First, make a BD according to these statements.

Conclusions:

1. Some writers are singers

2. Some actors are not dancers

3. All poets being actor is a possibility

4. No poet is a dancer

See the BD, 

Conclusion 1 clearly follows.

Also, some actors, which are singers (Red Portion), cannot be dancers. 

So, Conclusion 2 also follows.

But, what about Conclusion 3?

Let’s make a MD.

See the MD, 

Conclusion 3 clearly follows.

Also, since no singer is a dancer, so, no poet is a dancer. 

Hence, Conclusion 4 is also following!

• 1? Follows
• 2? Follows
• 3? Follows
• 4? Follows

Understood?