Syllogism for SBI PO

Syllogism is one of the few reasoning topics where a well-drilled candidate is almost never wrong. There are only five statement types, two kinds of conclusion and one method. Once the method is automatic, a question takes 30 to 40 seconds, which is why it belongs in the first few minutes of your prelims reasoning section.

The marks slip away in two places: forgetting what "only a few" rules out, and confusing "this must be true" with "this could be true". This guide fixes both.

How it is asked

In the prelims, syllogism usually comes as a small set of questions: two or three statements, two conclusions, and the familiar options (only I follows, only II follows, either I or II, neither, both). In the mains it can appear in a reversed form, where you are given the conclusions and must choose which set of statements supports them. The mix changes from year to year, so check two or three recent papers.

Two rules hold for every version:

• Take the statements as true, even if they sound absurd. "All rivers are chairs" is fine.
• Use nothing outside the statements. Real-world knowledge is the most common reason for a wrong answer.

The five statement types

"Only a few" is two statements in one. It gives you "some A are B" and it forbids "all A are B". Most mistakes on this type come from remembering the first half and forgetting the second.

What follows automatically

Some conclusions follow from a single statement by conversion. Learn this table, because it settles many questions without a diagram.

Definite and possibility conclusions

• A definite conclusion ("Some A are C") must be true in every diagram that fits the statements.
• A possibility conclusion ("All A being C is a possibility") needs only one diagram that fits the statements and makes it true.

So for a definite conclusion, you hunt for a diagram that breaks it. For a possibility, you hunt for a diagram that allows it. A possibility fails only when a statement forbids it: a "No" between the two terms, an "only a few", or a chain that forces them apart.

Either–or pairs

Sometimes neither conclusion follows, but one of them must be true. That is an either–or pair. Three conditions must all hold:

1. Both conclusions use the same two terms.
2. Neither follows on its own.
3. Together they cover every case. The usual pairs are "Some A are B" with "No A is B", and "All A are B" with "Some A are not B".

The five-step method

1. Draw the minimal diagram. Show only what the statements force: overlaps where "some" says so, containment where "all" says so, a gap where "no" says so.
2. Mark the fixed parts. Shade or tick the regions that must exist, such as the overlap created by "some".
3. Test each definite conclusion by trying to draw a legal diagram where it fails.
4. Test each possibility conclusion by trying to draw a legal diagram where it holds.
5. Check for either–or only when both conclusions have failed and they use the same two terms.

Worked examples

Example 1. Statements: All cheques are documents. Some documents are forms.

Conclusions: I. Some cheques are forms. II. Some forms are documents.

• The forms can overlap the part of documents that holds no cheques. So I is not certain.
• "Some documents are forms" converts to "some forms are documents". II follows.
• Only II follows.

Example 2. Statements: Only a few banks are branches. All branches are offices.

Conclusions: I. Some banks are offices. II. All banks being branches is a possibility.

• The banks that are branches sit inside offices, so some banks are offices. I follows.
• "Only a few" says some banks are not branches. II is ruled out.
• Only I follows.

Example 3. Statements: Some cards are coins. Some coins are notes.

Conclusions: I. Some cards are notes. II. No card is a note.

• Cards and notes may or may not overlap, so neither conclusion is certain.
• Same two terms, and "some" with "no" covers every case.
• Either I or II follows.

Example 4 (three statements). Statements: All loans are assets. Some assets are bonds. No bond is a share.

Conclusions: I. Some assets are not shares. II. All loans being shares is a possibility.

• The assets that are bonds cannot be shares, so some assets are not shares. I follows.
• Loans must stay inside assets, and shares must stay away from bonds. Nothing stops the loans sitting in the part of assets outside bonds, fully inside shares. II follows.
• Both follow.

Example 5. Statements: No pen is a marker. All markers are brushes.

Conclusions: I. Some brushes are not pens. II. Some pens being brushes is a possibility.

• Every marker is a brush and no marker is a pen. So the markers are brushes that are not pens. I follows.
• Pens must avoid markers, but can overlap the rest of the brushes. II follows.
• Both follow.

Common mistakes

• Reading "only a few" as plain "some", then marking "all A being B is a possibility" as true.
• Chaining two "some" statements. "Some A are B" and "some B are C" give nothing definite about A and C.
• Converting "some not". It never converts.
• Marking either–or with different terms, such as "Some A are B" with "No B is C".
• Drawing too much. A diagram with extra overlaps makes conclusions look definite when they are not.

Practice set

1. All pens are markers. Only a few markers are brushes. I. Some pens are brushes. II. All pens being brushes is a possibility.
2. Some savings are deposits. No deposit is a loan. I. Some savings are not loans. II. All loans being savings is a possibility.
3. All clerks are officers. All officers are staff. I. All clerks are staff. II. Some staff are clerks.
4. No book is a file. Some files are notes. I. Some notes are not books. II. Some books are notes.
5. Some cards are keys. Some keys are locks. No lock is a door. I. Some keys are not doors. II. Some cards are locks. III. No card is a lock.
6. Only a few pens are blue. All blue things are inks. I. All pens being inks is a possibility. II. Some inks are not pens.
7. All rates are ratios. No ratio is a fraction. I. No rate is a fraction. II. Some fractions being rates is a possibility.
8. Some forms are not files. All files are records. I. Some forms are not records. II. All records being forms is a possibility.

Answers:

1. Only II. Pens may miss the brushes entirely, so I is not certain. They can all sit in the part of markers that are brushes, because "only a few" needs only some markers outside brushes.
2. Both. The savings that are deposits are not loans, so I follows. Loans can lie in the part of savings outside deposits, so II is possible.
3. Both. Clerks sit inside officers, which sit inside staff. "All clerks are staff" then converts to "some staff are clerks".
4. Only I. The notes that are files cannot be books, so some notes are not books. Books and notes may or may not meet, so II is not certain.
5. I, and either II or III. The keys that are locks cannot be doors, so I follows. Cards and locks may or may not overlap, and II and III are a "some" and "no" pair on the same terms.
6. Only I. The pens that are not blue can still be inks, so I is possible. All the blue things could lie inside pens, with inks no bigger than that, so II is not certain.
7. Only I. Rates sit inside ratios, which never meet fractions. II is impossible, not just uncertain.
8. Only II. The forms outside files could still be records, so I is not certain. Records can lie wholly inside forms as long as some forms are left outside files, so II is possible.

What to do next

• Rewrite the "what follows" table from memory, then check it.
• Solve 20 syllogisms a day for a week, drawing a diagram for every one. Aim for 90% accuracy before chasing speed.
• Log every wrong answer by type: "only a few", possibility, either–or or conversion.
• Pair this with inequality, the other quick scorer, and see the reasoning plan for where both fit in your week.