Syllogism (including only-a-few) for IBPS PO

Syllogism questions look like vocabulary, but they are really a test of discipline. Your job is not to decide what sounds sensible. It is to decide what the statements force to be true, and what they merely allow. Most wrong answers come from mixing those two up.

IBPS PO syllogisms add two twists to the textbook version: the "only a few" statement and the possibility conclusion ("All A being B is a possibility"). Both are easy once you treat every question as a search for a diagram that breaks the conclusion.

What each statement means

Think of every term as a circle. Each statement tells you something about how two circles sit.

Two points trip people up.

• "Some A are B" does not say that some A are not B. All A may well be B.
• "Only a few A are B" is about A only. It says nothing about whether some B lie outside A. So "Some B are not A" does not follow from it.

Definite and possible conclusions

A definite conclusion ("Some A are B", "No A is B") follows only if it is true in every diagram that fits the statements. To reject it, you need just one valid diagram where it fails.

A possibility conclusion ("All A being B is a possibility") follows if at least one valid diagram makes it true. To reject it, you must show that the statements forbid it.

Three quick checks settle most possibility conclusions:

• A possibility fails if a statement directly contradicts it. "No A is B" kills "Some A being B is a possibility".
• "Only a few A are B" kills "All A being B is a possibility", because some A must stay outside B.
• If a conclusion is already definite, its possibility form also follows.

The either-or case

Sometimes neither conclusion is certain, but one of them must be true in every diagram. This happens when the two conclusions:

• are about the same two terms, and
• cover every situation between them: "Some A are B" and "No A is B", or "All A are B" and "Some A are not B".

Then the answer is "either I or II follows". Both conclusions must fail individually first. If one already follows, the either-or option is wrong.

Worked examples

Example 1

Statements: All pens are pencils. Some pencils are erasers.

Conclusions: I. Some pens are erasers. II. All pens being erasers is a possibility.

• I: Draw pens inside pencils, and the erasers overlapping only the part of pencils outside pens. Every statement holds and no pen is an eraser. I does not follow.
• II: Now stretch erasers to cover all of pens. Still valid. II follows.
• Answer: only II.

Example 2

Statements: Only a few books are novels. No novel is a magazine.

Conclusions: I. Some books are not magazines. II. All books being magazines is a possibility. III. All novels are books.

• I: The books that are novels can never be magazines. I follows.
• II: Those same books block it. II does not follow.
• III: "Only a few books are novels" is about books. Novels may extend outside books. III does not follow.
• Answer: only I.

Example 3: three statements

Statements: Some cups are plates. No plate is a spoon. All spoons are forks.

Conclusions: I. Some forks are not plates. II. Some cups are not spoons. III. Some forks are cups.

• I: Every spoon is a fork and no spoon is a plate, so those forks are not plates. I follows.
• II: The cups that are plates cannot be spoons. II follows.
• III: Forks and cups are never linked by a positive statement. Draw them apart and every statement holds. III does not follow.
• Answer: I and II.

Example 4: either-or

Statements: All lakes are ponds. Some ponds are wells.

Conclusions: I. Some lakes are wells. II. No lake is a well.

• I fails when wells touch only the part of ponds outside lakes.
• II fails when wells reach into lakes.
• In every diagram, lakes and wells either share a member or they do not.
• Answer: either I or II.

Example 5: possibilities with a negative

Statements: No bank is a shop. Only a few shops are malls.

Conclusions: I. Some malls are not banks. II. All malls being shops is a possibility. III. Some banks being malls is a possibility.

• I: Some shops are malls, and those malls cannot be banks. I follows.
• II: "Only a few shops are malls" limits shops, not malls. All malls can sit inside shops. II follows.
• III: Malls may extend outside shops, and that part can overlap banks without breaking "No bank is a shop". III follows.
• Answer: all three follow.

Common mistakes

• Treating "only a few" like "some". It also rules out "all".
• Reading "only a few A are B" backwards. It limits A, not B.
• Marking a possibility as definite. "Could be" is not "must be".
• Choosing either-or when one conclusion already follows, or when the two conclusions are about different pairs of terms.
• Bringing in real-world sense. If the statements say all cats are dogs, work with that.

Practice set

1. Statements: All singers are dancers. No dancer is a painter. Conclusions: I. No singer is a painter. II. Some painters being singers is a possibility.
2. Statements: Some keys are locks. Some locks are doors. Conclusions: I. Some keys are doors. II. No key is a door.
3. Statements: Only a few roses are red. All red things are bright. Conclusions: I. Some roses are bright. II. All roses being red is a possibility.
4. Statements: All tigers are cats. Some cats are dogs. No dog is a lion. Conclusions: I. Some cats are not lions. II. All tigers being dogs is a possibility.
5. Statements: No phone is a laptop. Some laptops are tablets. Conclusions: I. Some tablets are not phones. II. Some phones being tablets is a possibility.
6. Statements: Only a few pens are blue. Only a few blue things are ink. Conclusions: I. Some pens are ink. II. All ink being blue is a possibility. III. Some blue things are not pens.
7. Statements: All coins are metals. All metals are solids. Some solids are soft. Conclusions: I. All coins are solids. II. Some soft things being coins is a possibility.

Answers

1. Only I. Singers sit inside dancers, and dancers never meet painters, so no singer is a painter. That same fact forbids II.
2. Either I or II. Keys and doors are linked only through locks, so neither is certain, but one of the pair must hold.
3. Only I. The red roses are bright. "Only a few" keeps some roses outside red, so II fails.
4. I and II. The dogs among cats are not lions, so I follows. Tigers can sit inside the dog part of cats, which breaks no statement, so II follows.
5. I and II. The tablets that are laptops cannot be phones. Tablets outside laptops can overlap phones.
6. Only II. Pens and ink meet only through blue, and the two blue areas need not overlap, so I fails. "Only a few blue things are ink" limits blue, not ink, so all ink can be blue. III fails because "only a few pens are blue" says nothing about blue things outside pens.
7. I and II. Coins sit inside metals, which sit inside solids. Soft things can overlap solids exactly where coins are.

What to do next

• Redo the five worked examples without looking, drawing the one diagram that breaks each rejected conclusion.
• Solve ten syllogism questions a day for a week, and time yourself at about 40 seconds each.
• Then move to inequalities, the other quick-scoring topic, and revise the reasoning plan for where both fit in the section.