Syllogism: draw the possibility, do not trust the wording

Syllogism is three to five questions in a bank prelims reasoning section, and it should be close to a guaranteed set. The method is mechanical, the statements are short, and there is no puzzle to unravel. Yet it is quietly one of the most-dropped topics, because candidates answer from the wording of the conclusions instead of from a diagram, and the setters build every question around exactly that habit.

The rule that matters is simple to state and hard to obey under pressure: a conclusion follows only if it is true in every diagram the statements permit. One counter-diagram is enough to reject it.

Translate the statements into circles first

Never read the conclusions before you have drawn the statements. The conclusions are written to sound reasonable; the diagram cannot lie.

Each statement is one of four types, and each has a standard picture.

• All A are B. The A circle sits entirely inside the B circle.
• No A is B. Two separate circles that do not touch.
• Some A are B. Two overlapping circles, with the overlap being the “some”.
• Some A are not B. Overlapping circles where a definite part of A lies outside B.

Draw the statements together in one diagram, chaining on the common term. “All cats are animals. Some animals are pets” share the term animals, so the cats circle sits inside animals, and the pets circle overlaps animals somewhere.

The definite conclusions that always hold

A few chains produce conclusions you can rely on, and recognising them saves drawing time.

• All A are B, All B are C, therefore All A are C. Nesting is transitive.
• All A are B gives Some B are A. If every A is a B, then some Bs are certainly As. This conversion is the source of many correct “some” conclusions that look too easy to be true.
• No A is B gives No B is A. Negative statements convert directly.
• Some A are B gives Some B are A. Overlap is symmetric.

Everything else has to be tested against the possibility of an alternative diagram.

The possibility case is where the marks are

Here is the whole game. When a conclusion is not guaranteed by the chains above, ask whether you can draw a valid diagram in which it is false. If you can, it does not follow.

Take “Some A are B” and “Some B are C”. It is tempting to conclude “Some A are C”. But you can draw the A-B overlap and the B-C overlap on opposite sides of B, so that A and C never meet. That is a valid diagram in which “Some A are C” is false, so the conclusion does not follow. The wording invites the conclusion; the diagram refuses it.

This is why possibility cases are the entire topic. The setters choose statements precisely where an obvious-looking conclusion has a hidden counter-diagram.

Either-or: the pair that saves a whole question

When two conclusions are individually rejected but together they cover every case, the answer is “either-or”. The standard signal is a pair like “Some A are C” and “No A is C” built on the same terms. Neither follows on its own, because you can draw a diagram for each, but between them one must be true, so they form an either-or pair.

Two conditions must both hold: the two conclusions are made of the same subject and predicate, and each one fails on its own. When you see two conclusions that are direct opposites and you have already rejected both individually, check for either-or before marking “neither follows”. It is the most commonly missed answer in the topic.

Reverse syllogism and possibility conclusions

Newer papers add two variants, and both reward the same diagram habit.

Reverse syllogism gives the conclusions and asks which set of statements would produce them. Work backwards: take the option’s statements, draw them, and check that the given conclusions all hold. The correct option is the one whose diagram forces every stated conclusion.

Possibility conclusions ask whether something can be true rather than whether it must be. The test flips: a possibility follows if there is at least one valid diagram in which it is true. So read the conclusion carefully for the words “possibility” or “can be” — they invert the standard test, and a conclusion that would be rejected as a definite claim is accepted as a possibility.

Where the marks leak

Reading the conclusion before drawing. The root cause of almost every wrong answer. Draw first, always.

Testing only the obvious diagram. A conclusion that holds in your first sketch may fail in a second valid one. For any “some” or “some not” conclusion, deliberately try to draw a counter-example before accepting it.

Missing either-or. Rejecting both halves of a complementary pair and marking “neither” when the answer was “either-or”.

Confusing possibility with certainty. Marking a possibility conclusion wrong because it is not always true, when possibility only needs one supporting diagram.

Practice that transfers

Syllogism improves fastest when you force the diagram every single time, even on questions you think are obvious, because the whole failure mode is skipping the diagram on the easy- looking ones. For each question, draw the statements, then for every conclusion try to draw a diagram that breaks it before you decide.

Work through the syllogism and inequality practice set, which pairs statement-and-conclusion questions with the coded and direct inequalities that use the same “is it always true” discipline.