Syllogisms: "Follows" Is Not the Same as "True"
241 statement-and-conclusion questions here across thirty-eight exams. Almost every mark lost on them comes from answering a different question: whether the conclusion is true, rather than whether it follows.
A syllogism question gives you statements that are often absurd, then asks what follows from them. All pencils are erasers. No eraser is a pen. The statements are not claims about the world and you are not being asked to assess them. You are being asked a narrow question about whether a conclusion is forced by what you were given, and the 241 of these published on this site, across thirty-eight exams including IBPS RRB Office Assistant, IBPS RRB Officer Scale I, IBPS Clerk and RBI Assistant, are almost all got wrong in the same two ways.
- Accept the statements as given, however silly, and reason only from them.
- A conclusion follows only if it holds in every arrangement the statements allow. One counterexample arrangement kills it.
- "Some A are B" does not give you "some A are not B", because the statements also permit all of them being B.
- Draw the second arrangement, not the first. The first one you picture is the one that makes the wrong answer look right.
The first error: judging the conclusion
A conclusion reading "some fruits are not apples" is obviously true about the world, and the question is not asking about the world. If the statements you were given do not force it, it does not follow, and the answer is that it does not follow even though you know it is true. The reverse catches people too. A conclusion that sounds ridiculous can be perfectly valid given statements that are themselves ridiculous, and refusing it because it offends your knowledge of pencils is how a free mark gets thrown away.
The second error: picturing one arrangement
A set of statements usually permits several arrangements, and a conclusion has to hold in all of them. The trap is that one arrangement comes to mind immediately and the others take effort, so a conclusion true in the obvious picture looks forced when it is not. This is the whole mechanism behind the single commonest wrong answer in the format.
Why "some" is where the marks go
"Some A are B" means at least one A is a B. It says nothing about whether the rest of the A are B, so it is satisfied both by a partial overlap and by A sitting entirely inside B. In the overlap arrangement, "some A are not B" is true. In the nested arrangement, it is false. Since the statements permit the nested arrangement, the conclusion does not follow, and the fact that it feels like what "some" implies in conversation is exactly why the format uses it. The same applies in reverse: "some A are B" does always give you "some B are A", because at least one thing is in both and that is symmetric.
Draw the second arrangement, not the first. The first one you picture is the one that makes the wrong answer look right.
A procedure that fits inside a minute
- 1.Draw the statements as circles, taking the strongest reading each one allows. "All A are B" is A inside B. "No B is C" is two circles that do not touch. "Some A are B" is an overlap, with a note to yourself that A inside B is also allowed.
- 2.Read conclusion I against your drawing. If it holds, try to redraw the statements so that it fails. If you can, it does not follow.
- 3.Do the same for conclusion II, independently. The two conclusions are separate questions and a paper will often make one follow and not the other.
- 4.Pick from the four options, which on this site read "Only conclusion I follows", "Only conclusion II follows", "Both conclusions follow" and "Neither conclusion follows". Check their order on your own paper before the first question, because it varies.
The forms worth memorising
Three combinations cover most of what these questions test. Two universals in the same direction chain: all A are B, all B are C, so all A are C, and therefore some C are A. A universal affirmative with a universal negative gives a negative: all A are B, no B is C, so no A is C. And two "some" statements chain into nothing at all: some A are B and some B are C leaves it entirely open whether any A is a C. That last one is the form most often set, because it looks like it should produce something.
Where the "possibility" variant comes in
Some papers ask whether a conclusion is possibly true rather than whether it follows, and the logic inverts. A possibility holds if there is even one arrangement permitted by the statements in which the conclusion is true, so the work is to find a single arrangement rather than to rule all of them out. Reading the instruction line decides which question you are answering, and a candidate who has drilled only the standard form will answer the wrong one at speed.
How to practise it
This format rewards drilling more than most, because the skill is narrow and mechanical. Work a set and, for every conclusion you reject, draw the arrangement that defeats it rather than writing "does not follow". That drawing is the proof, and producing it is what makes the judgement fast enough for a paper allowing a 60-second median per question. Data sufficiency rewards the same discipline from the other direction, since both formats ask about what the given information forces rather than about the answer.
Syllogisms sit under whichever heading your paper gives its reasoning section, and reasoning has 23 names on Indian exam papers covers the naming. For whether to attempt one you are unsure of, understanding negative marking has the break-even for every scheme here. The exams setting them are in the exam directory.
Put the strategy into practice
Choose a checked mock test and apply what you learned while the idea is fresh.
Frequently asked questions
How do you solve syllogism questions?
Accept the statements as given, draw them as circles, and test each conclusion by trying to redraw the statements so the conclusion fails. If you can produce such an arrangement, the conclusion does not follow. Treat the two conclusions as separate questions, since papers frequently make one follow and not the other, and check the order of the four answer options before the first question because it is not consistent across papers.
Does "some A are B" mean "some A are not B"?
No, and this is the commonest wrong answer in the format. "Some A are B" means at least one A is a B and says nothing about the rest, so it is satisfied both by a partial overlap and by A sitting entirely inside B. Because the nested arrangement is permitted, "some A are not B" does not follow. The symmetric version does hold: "some A are B" always gives you "some B are A".
What if the conclusion is true but does not follow from the statements?
Then it does not follow, and that is the answer. These questions ask only whether the given statements force the conclusion, so your knowledge of the world is not evidence either way. The same applies in reverse: a conclusion that sounds absurd can be valid given absurd statements, and rejecting it on plausibility is a mark given away.
What is the difference between "follows" and "possibly follows"?
A conclusion follows if it holds in every arrangement the statements permit, so one counterexample arrangement defeats it. A conclusion possibly follows if it holds in at least one permitted arrangement, so finding a single arrangement establishes it. The two call for opposite work, and which one a question wants is in its instruction line rather than in the conclusions.