Syllogism for SSC CHSL

Syllogism questions give you two or three statements and some conclusions, and ask which conclusions definitely follow. The statements may be absurd ("All cats are cars"). You still treat them as true, and you ignore everything you know about the real world.

The key word is definitely. A conclusion that could be true is not enough. It must be true in every picture that fits the statements. That is why the reliable method is to draw the diagram, then try to break each conclusion with a different diagram that still fits.

How it is asked

A typical SSC CHSL item gives two statements and two conclusions, with options such as:

• Only conclusion I follows.
• Only conclusion II follows.
• Both I and II follow.
• Neither I nor II follows.

Some items add "Either I or II follows", and some give three statements and three conclusions. The method does not change.

The four statement types

What can be concluded directly

Two useful chains:

• All A are B + All B are C gives All A are C (and so Some C are A).
• Some A are B + All B are C gives Some A are C, because the A's that are B are inside C.

Two that do not work:

• All A are B + Some B are C does not give Some A are C. The C's may overlap only the part of B outside A.
• Some A are B + Some B are C gives nothing definite about A and C.

The method, step by step

1. Draw the simplest diagram that fits all the statements.
2. Test each conclusion on it. If it is false there, it does not follow. Stop.
3. If it is true, try to break it. Redraw, moving circles as far apart as the statements allow (or as close together), keeping every statement true. If any valid picture makes the conclusion false, it does not follow.
4. Only a conclusion true in every picture follows.
5. Check for an either–or pair among the conclusions that do not follow (see below).

Why step 3 matters: your first sketch is one case out of many. A conclusion that looks true in your sketch may only be true because of how you happened to draw it.

Either–or pairs

"Either I or II follows" is correct only when all three conditions hold:

• Neither conclusion follows on its own.
• Both conclusions are about the same two terms.
• Together they cover every case: one is "Some A are B" and the other "No A is B", or one is "All A are B" and the other "Some A are not B".

Six worked questions

Q1. Statements: All pencils are pens. Some pens are erasers.
Conclusions: I. Some pencils are erasers. II. Some erasers are pens.
I: draw the erasers overlapping only the part of pens outside pencils. Both statements still hold, and I is false, so I does not follow. II: "Some pens are erasers" reverses to "Some erasers are pens", so II follows. Answer: only II follows.

Q2. Statements: No book is a chair. All chairs are tables.
Conclusions: I. No book is a table. II. Some tables are chairs.
I: books may overlap the part of tables that are not chairs, so I does not follow. II: All chairs are tables, so some tables are chairs. Answer: only II follows.

Q3. Statements: All roses are flowers. All flowers are plants.
Conclusions: I. All roses are plants. II. Some plants are roses.
Roses sit inside flowers, which sit inside plants, in every picture. Answer: both follow.

Q4. Statements: Some boxes are bags. Some bags are bottles.
Conclusions: I. Some boxes are bottles. II. No box is a bottle.
Neither follows: boxes and bottles can overlap or stay apart. But the two conclusions are about the same terms, and one of them must be true in every picture. Answer: either I or II follows.

Q5. Statements: Some teachers are singers. No singer is a dancer.
Conclusions: I. Some teachers are not dancers. II. No teacher is a dancer.
The teachers who are singers cannot be dancers, so I follows. Other teachers may be dancers, so II does not follow. They are not an either–or pair, because I already follows. Answer: only I follows.

Q6. Statements: Some pens are books. All books are bags. No bag is a box.
Conclusions: I. Some pens are bags. II. No book is a box. III. Some pens are boxes.
I: the pens that are books are inside bags, so I follows. II: books are inside bags and bags share nothing with boxes, so II follows. III: pens outside books may or may not touch boxes, so III does not follow. Answer: only I and II follow.

Common traps

Practice

For each question, choose: (a) only I follows (b) only II follows (c) both follow (d) neither follows (e) either I or II follows.

1. All dogs are animals. All animals are living beings. I. All dogs are living beings. II. Some living beings are dogs.
2. Some pens are red. No red thing is blue. I. Some pens are not blue. II. Some blue things are pens.
3. All cups are plates. No plate is a spoon. I. No cup is a spoon. II. Some spoons are cups.
4. Some trees are fruits. Some fruits are flowers. I. Some trees are flowers. II. No tree is a flower.
5. All chairs are tables. All tables are desks. I. All desks are chairs. II. Some desks are tables.
6. No lion is a tiger. No tiger is a cat. I. No lion is a cat. II. Some cats are lions.
7. Some doctors are poets. All poets are singers. I. Some singers are doctors. II. All doctors are singers.
8. All boys are students. Some students are girls. No girl is a teacher. I. Some students are not teachers. II. Some boys are teachers.

Answers:

1. (c) Both. Dogs inside animals inside living beings in every picture.
2. (a) Only I. The pens that are red cannot be blue. Blue things may share nothing with pens.
3. (a) Only I. Cups are inside plates and plates share nothing with spoons, so no cup is a spoon, and II is then false.
4. (e) Either I or II. Neither follows alone, but they are a Some/No pair on the same terms.
5. (b) Only II. "All desks are chairs" reverses an "all" statement; "Some desks are tables" follows from "All tables are desks".
6. (e) Either I or II. Two "no" statements say nothing about lions and cats, and I and II are a No/Some pair.
7. (a) Only I. The doctors who are poets are singers. Other doctors may not be.
8. (a) Only I. The students who are girls are not teachers. Nothing links boys to teachers.

What to do next

• For every syllogism you practise this week, draw a second diagram that tries to break each conclusion.
• Learn the two chains that work and the two that do not; they settle most questions without a drawing.
• Solve 15 either–or questions and check each against the three conditions.
• Continue with Venn diagrams, which use the same circles for a different question type.