Important Formula: Syllogism | General Intelligence and Reasoning for SSC CGL PDF Download

Syllogism Formulas

Rules for solving Syllogism Questions

Navigating through various sentence types can pose challenges in reaching a specific conclusion. Nonetheless, if you possess a comprehensive understanding of the rules outlined below, coupled with their proper application, you are anticipated to make no errors when tackling the questions. Check out the below rules:

1. Universal Positive Statement

To start, the term "universal" denotes something applicable to all in a positive manner, akin to an affirmative format like 'yes.' A universal positive statement expresses a degree of positivity applicable to all elements within a given group. The positive category is represented by the alphabet 'A.' Such statements typically commence with words like All, Each, and Every. 

2. Universal Negative Statement
In this scenario, the primary distinction from the previous type is that, here, the sentence conveys a negative sense. This indicates that it pertains to sentences that are generic and convey a pessimistic expression. Such sentences typically commence with words like No, Not a single, None of the, and similar terms. These sentences are represented by the letter 'E.' 

3. Particular Positive Statement

In this situation, the given sentence offers a positive expression, however, it includes only a few things and not all. These kinds of sentences often starts with some, a few, any, and are symbolized by the letter ‘I’.

4. Particular Negative Statement

Here, the statement again covers only some items, but it gives a negative impression. These kinds of sentences are symbolizes by the letter ‘O’.

• When there are two specific sentences, no universal assumption is imaginable.
• When there are two positive sentences, no negative assumption is imaginable.
• When there are two negative sentences, no positive assumption is imaginable.
• When there are two specific sentences, no assumption can take place, apart from when an ‘I’ kind of sentence is provided as well as by retreating it an ‘I’ kind of assumption can be done.

Important Points

• Syllogism consists of three components: minor premise, major premise, and conclusion.
• Categorical syllogism typically encompasses these three elements.
• However, two additional key types of syllogism also exist.

Examples

Q1:

Statement:

Some messages are whatsapp.
1. All Hikes are whatsapp.
2. All whatsapp are facebook.

Conclusion:
1. Some facebook are messages
2. All hikes are facebook
3. Some messages are hikes
4. Some message are facebook

(a) Only 1 and 2 follows
(b)Only either 3 and 4 follows
(c) Only 1 and either 3 or 4 follows
(d) Only 1 2 and 4 follows
Ans: (d)
Clearly the statement makes it obvious that there is no relation between messages and hike hence statement 3 is incorrect.

Q2:
Statement:
To give an elite education to their children, parents today are ready to pay any amount.

Conclusion:
I.  All parents are very rich these days
II. Parents are obsessed for perfect development of their children.

(a) Only conclusion I follows
(b) Only conclusion II follows
(c) Either I or II follows
(d) Neither I nor II follows
Ans: (b)
The statement points that people are motivated towards providing their children an elite education. All parents are rich or not, it is not mentioned in the statement. Hence, only conclusion II follows and I does not.

Q3:
Statement:

I. All the harmoniums are instruments.

II. All the instruments are flutes.

Conclusion:

I. All the flutes are instruments.
II. All the harmoniums are flutes.

(a) Only conclusion I follows.
(b) Only conclusion II follows.
(c) Either I or II follows.
(d) Neither I nor II follows.
Ans: (b)
The statement points that all harmoniums are instruments , and all instruments are flutes but the reverse is not true hence only conclusion 2 is correct

Q4:
Statement:
I. Some cups are pots
II. All pots are tubes

Conclusion:
I. Some pots are cups
II. Some tubes are cups

(a) Only conclusion I follows
(b) Only conclusion II follows
(c) Either I or II follows
(d) Both I and II follows
Ans: (d)
The statement points that some cups are pots hence some pots are also cups and all pots are tubes therefore, some tubes can be cup also , so both the statement are true

Q5: 

Statements:
All Americans are English speaking.
No Eskimos are English speaking.

Conclusions:
I. No Eskimos are Americans.
II. No English-speakers are Eskimos.
(a) Only I follows
(b) Neither I nor II follows
(c) Only II follows
(d) Both I and II follow
Ans: (d)
We can align the premises by converting the second premise.
All Americans are English speaking. ↔ No English speakers are Eskimos.
We know that,
A + E → E type conclusion Thus, our derived conclusion would be:
“No Americans are Eskimos.”
Conclusion I is the converse of the derived conclusion.
Conclusion II is the converse of second premise.