Tips and Tricks: Syllogism | General Intelligence and Reasoning for SSC CGL PDF Download

Introduction

• Subject – The primary topic under discussion.
• Predicate – The segment that asserts something about the subject.

There are four statement types, each illustrated below with an example:

Type 1: All P is Q

It can be portrayed with the help of a Venn diagram:

From this we can definitely conclude that:

• All P’s are Q’s
• Some P’s are Q’s
• And some Q’s are P’s

But we cannot be sure that:

• All Q’s are P’s
• Some Q’s are not P’s

Type 2: No P’s are Q’s

From the diagram we can definitely conclude that:

• Some P’s are Q’s
• Some Q’s are P’s

Possible conclusion:

• All P’s are Q’s
• All Q’s are P’s
• Some P’s are not Q’s
• Some Q’s are not P’s.
  

Type 3: Some P’s are Q’s

From the diagram we can definitely conclude that:

• Some P’s are Q’s
• Some Q’s are P’s

Possible conclusion:

• All P’s are Q’s
• All Q’s are P’s
• Some P’s are not Q’s
• Some Q’s are not P’s.

Therefore, based on the diagrams provided earlier, we have compiled concise tips and tricks that should be memorized for solving Syllogism questions.

Definite cases: (For questions containing only two items)

• All+ All= All
• All+ No= No
• All+ Some= No conclusion
• Some+ All= Some
• Some+ No= Some Not
• Some+ Some= No conclusion

Possible cases:

1. If all P’s are Q’s that does not mean that all Q’s are P’s which means that some Q’s cannot be P.
   All P’s are Q’s—->Some Q’s are not P’s
2. If some Q’s are not P’s——->There is possibility that all P’s are not Q’s
3. If some P’s are Q’s——->There is possibility that all P’s are Q’s and all Q’s are P’s

Shortcut, Tips and Tricks to Solve Syllogism Problems

1. Verbal Method

The verbal method of elucidating syllogism questions is comparatively underutilized by test takers. In this approach, the test taker comprehends the set of premises and, relying on the capacity to grasp the assumptions, verbally deduces a conclusion. This technique is effective for less intricate questions.

For example

Statement I: Some human is rich.
Statement II: All rich are men.

Conclusion:

1. Some human is a man.
2. All men are rich.

Options:

1. The only Conclusion I follows
2. Only Conclusion II follows
3. Either conclusion I or Conclusion II follows
4. Neither conclusion I nor Conclusion II follows

Ans: 1
Sol:
From the above statements it is clear that some humans are rich and all rich are man, therefore there is a possibility that some some humans are man.

2. Venn Diagram method

The utilization of Venn diagrams permits the test taker to solve questions through a graphical approach, proving highly effective in addressing syllogism queries. This is illustrated well with the help of some bullet points mentioned below:

• Firstly we have to draw the diagram based on the given statements.
• Then we have to check which conclusion follow the given information, with the help of the diagram.
• If the Conclusion is fulfilling one condition but is not accomplishing the other conditions represented in the diagram, then it will not be considered as a conclusion.
• Hence the final conclusion should be made only if it follows all the possible conditions.

For example

Statement I: All P’s are Q’s
Statement II: All Q’s are R’s
Statement III: Some R’s are S

Conclusion:

• All P are R
• No Q are R
• All S are R

Options:

1. The only Conclusion I follows
2. Only Conclusion II follows
3. Either conclusion I or Conclusion II follows
4. Neither conclusion I nor Conclusion II follows

Ans: 1
Sol:
The last diagram is the final one, and based on this we will draw conclusions.

Conclusion:

• All P are R
• No Q are R
• All S are R

Conclusion 1 is true as Circle representing P is completely inside circle representing R
Conclusion 2 is false as circle representing Q is completely inside circle representing R.
Therefore there is no possibility that no Q are R.
Conclusion 3 is also not true because some part of S is some part of R.
Therefore we can say that only conclusion 1 follows.
Hence option 1 is the correct one.

For Example

Statements :
No singers are actors.
Some actors are artists.
No artist is artisan.

Conclusions :
I. Some artists are not singers.
II. Some artisans are not actors.

Options

1. Neither conclusion I nor conclusion II follows
2. Only conclusion I follow
3. Only conclusion II follow
4. Both the conclusions follow

Sol:
Analyzing Conclusion I : Some artists are not singers.
Some artists are actors (reverse of Statement 2) + No actor is singer (reverse of Statement 1)
= Some artists are not singers. Clearly, Conclusion 1 follows.
Analyzing Conclusion II :
Some actors are artists + No artist is artisan
= Some actors are not artisans. Since reverse of an Partial Negative statement is not possible, Conclusion 2 doesn’t follow.

For Example

Statements :
All wells are rivers.
All seas are rivers.
Some rivers are not seas.

Conclusions :
I. Some wells are not seas.
II. Some seas may not be rivers.

Options

1. Neither conclusion I nor conclusion II follows
2. Only conclusion I follow
3. Only conclusion II follow
4. Both the conclusions follow

Sol:
Analyzing Conclusion I: Some wells are not seas.
Neither Statement 1 nor 2 is a negative statement.
So, negative conclusion between the classes of ‘wells’ and ‘seas’ is not possible. Hence, Conclusion 1,doesn’t follow.
Analyzing Conclusion II: Some seas may not be rivers.
In Statement 3 : ‘Some rivers are not seas’. Here, we are not sure of the elements of the class ‘seas’. So, it means that ‘Some seas may not be rivers’.
Conclusion 2, hence, follows.

Examples

Direction: In each of the question below are three statements following by three conclusions numbered I, II and III. You have to take the three given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusion logically follows from the two statements disregarding commonly known fact.

Example1: 

Statement:
All pins are rods. Some rods are chains. All chains are hammers.

Conclusions:
I. Some pins are hammers.
II. Some hammers are rods
III. No pin is hammer.

(a) Only I follows
(b) Only II follows
(c) Only III follows
(d) Only either I or III & II follows
Ans: (d)
All pins are rods + Some rods are chains = A + I = No conclusion Hence I and II does not follow. However, the two a complementary I-E pair, Hence either I or III follows. Some rods are chains + All chains are Hammers = I + A + I = Some rods are hammers → conversion → Some hammers are rods (I). Hence III follows.

Example2:
Statement:
Some pots are buckets. All buckets are tubs. All tubs are drums.

Conclusions:
I. Some drums are pots.
II. All tubs are buckets.
II Some drums are buckets.

(a) Only I and II follows
(b) Only I and III follows
(c) Only II and III follows
(d) All  follows
Ans: (b)
All buckets are tubs(A) → conversion ⇒ Some tubs are buckets (I) Hence II does not follow. All buckets are tubs + All tubs are drums A + A = A = All buckets are drums → conversion → Some drums are buckets + All buckets are drums = A + A + I + = Some drums are pots(I). Hence II follows.

Example3:

Statement:
Some buses are trucks. Some trucks are boats. No boat is jeep.

Conclusions:
I. Some jeeps are buses.
II. Some boats are buses.
III. Some jeeps are trucks.

(a) Only I follows
(b) Only II follows
(c) Only III follows
(d) None follows
Ans: (d)
Some buses are trucks + Some trucks are boats = I + I = No conclusion Hence II and consequently do not follow Some trucks are boats + No boat is jeep = I + E = O = Some trucks are not jeeps. Hence III does not follow.

Example 4:

Statement:
Some books are papers. Some papers are desks. All desks are chairs.

Conclusions:
I. Some books are desks.
II. Some papers are chairs.
III. Some books are chairs.

(a) None follows
(b) Only I follows
(c) Only II follows
(d) Only III follows
Ans: (a)
I-type statements can't be combined.

Example 5:
Statement:
All pins are bags. All chalks are bags. All needles are bags.

Conclusions:
I. Some needles are pins.
II. Some chalks are needles.
III. No needle is pin.

(a) Only I follows
(b) Only III follows
(c) Only either I or III follows
(d) Only either I or III and II follows
Ans: (c)
All pins are bags (A) → conversion → Some bags are pins (I). All needles are bags + Some bags are pins = A + I = No conclusion Hence I and III do not follow by combination. However, they from an complementary E-I pair, either I or III follows. Again, All chalks are bags + conversion of all needles are bags = A + I = No conclusion Hence II do not follow.