SSC CHSL Reasoning Syllogism: Rules and Special Cases

Syllogism is one of the most frequently asked topics in the SSC CHSL Reasoning section. Questions are generally based on Venn diagrams, logical relationships, and conclusion-based reasoning. 

Along with basic syllogism rules, candidates should also understand special cases such as Only A are B, Only a Few A are B, and possibility-based questions, as these concepts are regularly tested in SSC examinations. Mastering these rules improves both speed and accuracy during the exam. 

Syllogism Special Cases

Syllogism questions are a regular feature in competitive exams like SSC CGL and CHSL. While basic rules and "Either-Or" conditions are fundamental, understanding special cases is increasingly vital. 

These specific constructions, "Only A are B" and "Only a Few A are B," often deviate from standard positive/negative inferences, requiring a distinct approach for accurate solutions.

Warm-up Question: Possibility

This section reviews a possibility question to set the context for advanced cases.

Statements:

1. Some monkeys are gorillas.

2. All Gorillas are Black.

Conclusions:

1. All Monkey Are Black Being A Possibility.

2. All Gorillas Can Be Monkeys.

Explanation:

• Conclusion 1: The portion of "Monkey" not overlapping with "Gorilla" can potentially move entirely into "Black." Hence, this possibility is correct.

• Conclusion 2: Given "Some Monkeys are Gorilla," it is possible for the entire "Gorilla" set to be within "Monkey." This possibility is correct.

• Both conclusions are correct.

Special Cases in Syllogism

Competitive exams often feature three primary special cases that do not follow traditional direct inference rules:

1. Only A are B (केवल ए बी हैं)

2. Only a Few A are B (केवल ही कुछ ए बी हैं)

3. A Few A are B (कुछ ही A B हैं)

Understanding "A Few A are B"

The phrase "A Few A are B" is a straightforward representation that means "Some A are B".

• This implies "Some A are B" and, consequently, "Some B are A".

• No other specific direct conclusions can be drawn solely from this statement.

Understanding "Only a Few A are B"

This is a very important special case. The statement "Only a Few A are B" always implies two distinct conclusions:

1. Some A are B. (कुछ A B हैं)

2. Some A are Not B. (कुछ A B नहीं हैं)

Valid Direct Conclusions from "Only a Few A are B":

• Some A are B. (Correct)

• Some A are Not B. (Correct)

• Some B are A. (Correct, as the converse of "Some A are B")

Invalid Direct Conclusions from "Only a Few A are B":

• All B are A. (Incorrect)

• All A are B. (Incorrect, as "Some A are Not B" is true)

• Some B are Not A. (Incorrect, as the relationship for B to A is not explicitly defined)

• No A is B / No B is A. (Incorrect, as "Some A are B" is true)

Example: Only a Few Door Are Wall

Statement: Only a Few Door are Wall.

Conclusions:

1. All Door are Wall. (Incorrect, because "Some Door are Not Wall" is implied.)

2. No Door is Wall. (Incorrect, because "Some Door are Wall" is implied.)

3. Some Door are Not Wall. (Correct)

4. Some Door are Wall. (Correct)

5. No Wall is Door. (Incorrect, as "Some Wall are Door" is true.)

6. Some Wall are Door. (Correct)

Example: Student, Teacher, Lecturer

Statements:

1. Only a Few Student are Teacher.

2. Some Teacher are Lecturer.

Conclusions:

1. Some Student are Lecturer. (Incorrect, "Can't Say" directly from the diagram.)

2. No Student is Teacher. (Incorrect, contradicts "Only a Few Student are Teacher" which implies "Some Student are Teacher.")

Example: Tickets, Watch, Button

Statements:

1. Only a Few Tickets are Watch.

2. Some Button are Ticket.

Conclusions:

1. No Ticket is Stamp. (Incorrect, "Stamp" is an external, unrelated term; direct inference not possible.)

2. Some Button are Watches. (Incorrect, no guaranteed direct overlap between "Button" and "Watch.")

Example: Telescope, Periscope, Microscope

Statements:

1. Only a Few Telescope are Periscope.

2. Some Telescope are Microscope.

Conclusions:

1. Some Periscope are Microscope. (Incorrect, no direct overlap.)

2. Some Microscopes are Telescope. (Correct, converse of "Some Telescope are Microscope.")

Example: File, Folder, PDF

Statements:

1. Only a Few File is Folder.

2. Some Files are PDF.

Conclusions:

1. Some PDF are Folder. (Incorrect, no direct overlap.)

2. Some PDF are File. (Correct, converse of "Some Files are PDF.")

Understanding "Only A are B"

This is a critical and unique case. The statement "Only A are B" (केवल ए बी हैं) must be rewritten and interpreted as "All B are A."

Rewriting and Diagramming:

• Rewrite "Only A are B" as "All B are A".

• Diagram: Draw the circle for B entirely inside the circle for A.

• The Concept of "Star" (Exclusivity): To signify the unique property, a star is placed on the element that was originally after "Only" (i.e., B in "Only A are B").

• (Memory Tip: This "star" signifies an exclusive relationship, meaning B has a relation only with A and with no other element outside A. No other element can directly or indirectly relate to B without going through A.)

Example: Only Cat Are Rabbit

Statement: Only Cat are Rabbit.

Rewritten: All rabbits are cats.

Diagram: "Rabbit" circle inside "Cat" circle, with a star on Rabbit.

Conclusions:

1. All Cats are Rabbit. (Incorrect)

2. No Cat is Rabbit. (Incorrect)

3. Some Cats are Not Rabbit. (Incorrect)

4. Some Cats are Rabbit. (Correct)

5. All Rabbits are Cat. (Correct)

6. Some Rabbits are Cat. (Correct, derived from "All Rabbits are Cat")

Example: Only Book Are Pencil (with No relationship)

Statements:

1. Only Book are Pencil.

2. No Book is Cat.

Explanation:

• Rewrite Statement 1 as "All Pencil are Book" with a star on Pencil.

• Since "Pencil" (the starred element) has an exclusive relationship only with "Book," and "Book" has "No" relationship with "Cat," it implies that Pencil can also have no relationship with Cat.

Conclusions:

1. Some Books are Cats. (Incorrect, contradicts Statement 2.)

2. Some Pencils are Cats. (Incorrect, due to the exclusive nature of starred "Pencil" with "Book," and "Book's" separation from "Cat.")

3. No Pencil is Cat. (Correct)

4. Some Books are Not Cats. (Correct, implied by "No Book is Cat.")

Example: T, F, P (Combined with Possibility)

Statements:

1. Only T are F.

2. Some F are P.

Explanation:

• Rewrite Statement 1 as "All F are T" with a star on F.

• Due to the star on F, P can only relate to F within F's relationship with T. P cannot directly relate to T without going through F.

Conclusions (Direct):

1. Some P are T. (Incorrect, "Can't Say" directly.)

2. No F is T. (Incorrect, contradicts "All F are T.")

3. No T is P. (Incorrect. As some F are P, and F is within T, some T are P. Thus, "No T is P" is false.)

4. Some F is Not P. (Correct, implied by "Some F are P.")

Conclusions (Possibility):

1. All F Being P is a Possibility. (Incorrect. Because F is starred, it's exclusively within T. If all F were P, and P has parts outside T, this would violate F's exclusive relation to T.)

2. All T Being P is a Possibility. (Incorrect. T cannot fully include P because T contains F, and starred F has an exclusive relation with T. T cannot expand to include all of P if P contains elements unrelated to T, without violating F's exclusivity.)

3. All P Being F is a Possibility. (Correct. All elements of P can potentially be part of F, as long as F itself remains within T. This does not violate the exclusivity of the starred element F.)

Key Rule for Possibility in Syllogism

A crucial rule for possibility conclusions:

• Any conclusion that is already definitely true (100% true) based on direct inference cannot be considered a possibility. Such a possibility statement will always be marked incorrect.

• For example, if "Some A are B" is already confirmed as true from the statements, then stating "Some A are B is a possibility" is incorrect.