Syllogism Questions: Rules, Valid Forms and Common Traps
A syllogism question gives you two (sometimes three) statements such as "All managers are employees" and "Some employees work remotely", and asks which conclusion must follow; often the right answer is that nothing definite follows. You solve them by checking whether the middle term links the other two terms in every possible case, either with a few distribution rules or with a quick Venn diagram. Below are the four statement types, the five rules, the valid forms worth knowing, the traps test writers rely on, and eight practice questions with explained answers.
The structure of a syllogism
A categorical syllogism has three terms and three statements:
- Premise 1: links term A to the middle term B.
- Premise 2: links the middle term B to term C.
- Conclusion: links A and C directly. B does not appear.
"All mammals are animals. All dogs are mammals. So all dogs are animals." The middle term is mammals: it appears in both premises and disappears in the conclusion. If the middle term does not tie the two outer groups together, no conclusion follows, however plausible one sounds.
The four statement types
| Statement | Name | Diagram | Distributes |
|---|---|---|---|
| All A are B | Universal affirmative (A) | A circle entirely inside B | A |
| No A are B | Universal negative (E) | A and B do not overlap | A and B |
| Some A are B | Particular affirmative (I) | At least one item in the overlap | Neither |
| Some A are not B | Particular negative (O) | At least one A outside B | B |
A term is distributed when the statement says something about every member of that group. "All A are B" tells you about every A, but not about every B. "Some A are not B" tells you that every B is excluded from that particular A, which is why it distributes B. In tests, "some" means "at least one, possibly all". It does not imply "but not all".
The five rules of validity
- The middle term must be distributed at least once. "All A are B. All C are B." Both premises only talk about part of B, so A and C may or may not overlap. Invalid.
- A term distributed in the conclusion must be distributed in its premise. You cannot go from "some" in a premise to "all" or "no" in the conclusion.
- Two negative premises give no conclusion. "No A are B. No B are C." A and C could overlap completely or not at all.
- A negative premise requires a negative conclusion, and vice versa.
- A particular premise requires a particular conclusion. One "some" in the premises means the conclusion can only be a "some" statement.
If a candidate conclusion breaks any rule, eliminate it. If all options break a rule, the answer is "no conclusion follows".
Valid forms worth recognising
| Form | Premises | Conclusion |
|---|---|---|
| Barbara | All M are P. All S are M. | All S are P. |
| Celarent | No M are P. All S are M. | No S are P. |
| Darii | All M are P. Some S are M. | Some S are P. |
| Ferio | No M are P. Some S are M. | Some S are not P. |
| Camestres | All P are M. No S are M. | No S are P. |
You do not need the Latin names. What helps is recognising the shape: All + All gives All, No + All gives No, All + Some gives Some, No + Some gives Some ... not.
Worked example with a Venn diagram
Premises: No engineers are lawyers. Some lawyers are writers. Options: (a) Some writers are engineers. (b) No writers are engineers. (c) Some writers are not engineers.
- Draw three overlapping circles: Engineers, Lawyers, Writers.
- "No engineers are lawyers" is universal: shade the whole overlap of Engineers and Lawyers, including the part inside Writers.
- "Some lawyers are writers" is particular: place an X in the Lawyers–Writers overlap. The part of that overlap that is also inside Engineers is shaded, so the X goes in the region that is Lawyer and Writer but not Engineer.
- Read the result. There is a writer who is not an engineer, so (c) is forced. Nothing tells you whether any writer is an engineer, so (a) and (b) are both possible but not certain.
Always draw universal premises before particular ones. Shading first tells you exactly where the X must go.
Typical traps
Illicit conversion. "All A are B" does not mean "All B are A". All pilots are licensed, but not all licensed people are pilots. Conversion works only for "No" and "Some ... are": "No A are B" equals "No B are A", and "Some A are B" equals "Some B are A". "Some A are not B" cannot be reversed.
Undistributed middle. "All pilots are licensed. Some licensed people are instructors." The instructors might be entirely outside the pilots. Test writers love this because "Some pilots are instructors" sounds natural.
Reading "some" as "some but not all". If the premise says "Some analysts are graduates", the conclusion "Some analysts are not graduates" does not follow. All analysts might be graduates.
Real-world knowledge. Questions often use plausible or deliberately absurd content. Judge the form, not the facts.
The existential trap. From "All A are B" alone, do not conclude "Some A are B" unless the test states that every group has members. Most modern tests avoid relying on this, so treat such options with suspicion.
Time strategy
Most syllogism items can be done in 30–60 seconds once the rules are familiar.
- 0–10 seconds: identify the middle term and the statement types.
- 10–30 seconds: apply the quick checks. Two negatives? Undistributed middle? Particular premise? Each one eliminates options immediately.
- 30–60 seconds: if two options remain, sketch the three circles. Shade universals, place the X, read the answer.
- Over 90 seconds: pick the option that respects the rules, flag it and move on.
The most efficient habit is to decide what could follow before reading the options. Options are written to sound reasonable, and reading them first pulls you towards the plausible one.
Practice questions
Question 1
All managers are employees. All employees have a staff ID. Which conclusion follows?
A) All managers have a staff ID. B) Everyone with a staff ID is a manager. C) Some employees are not managers. D) No conclusion follows.
Answer: A. This is the All + All form. B is an illicit conversion, and C is not stated: every employee could be a manager.
Question 2
No cats are reptiles. All lizards are reptiles. Which conclusion follows?
A) Some lizards are cats. B) No lizards are cats. C) All reptiles are lizards. D) No conclusion follows.
Answer: B. Every lizard is inside the reptile circle, and the reptile circle does not touch the cat circle, so no lizard can be a cat.
Question 3
All pilots are licensed. Some licensed people are instructors. Which conclusion follows?
A) Some pilots are instructors. B) Some instructors are pilots. C) No pilots are instructors. D) None of these conclusions follows.
Answer: D. The middle term "licensed" is never distributed. The instructors may or may not include pilots, so neither A, B nor C is forced.
Question 4
Some analysts are graduates. All graduates passed the entry test. Which conclusion follows?
A) All analysts passed the entry test. B) Some people who passed the entry test are not analysts. C) Some analysts passed the entry test. D) No conclusion follows.
Answer: C. The analysts who are graduates all passed. A overstates it, and B is unsupported: everyone who passed might be an analyst.
Question 5
No engineers are lawyers. Some lawyers are writers. Which conclusion follows?
A) Some writers are engineers. B) No writers are engineers. C) Some writers are not engineers. D) Some engineers are not writers.
Answer: C. The writers who are lawyers cannot be engineers. D looks like a mirror image but is not supported: every engineer could also be a writer.
Question 6
Some applicants are not bilingual. All translators are bilingual. Which conclusion follows?
A) Some translators are not applicants. B) Some applicants are not translators. C) No applicants are translators. D) No conclusion follows.
Answer: B. An applicant who is not bilingual cannot be a translator, because every translator is bilingual. C is too strong: other applicants may be bilingual translators.
Question 7
No auditors are sales staff. No sales staff are part-time. Which conclusion follows?
A) No auditors are part-time. B) Some auditors are part-time. C) Some auditors are not part-time. D) No conclusion follows.
Answer: D. Two negative premises never produce a conclusion. Auditors and part-time workers could overlap fully, partly or not at all.
Question 8
All consultants are graduates. No graduates are interns. Some trainees are interns. Which conclusion follows?
A) Some trainees are consultants. B) No trainees are consultants. C) Some trainees are not consultants. D) All consultants are trainees.
Answer: C. From the first two premises, no consultants are interns. The trainees who are interns therefore cannot be consultants. B is too strong, because trainees who are not interns could still be consultants.
A one-week practice plan
| Day | Focus |
|---|---|
| 1 | Learn the four statement types and what each distributes. Draw each as a Venn diagram |
| 2 | Ten All/No items. Spot illicit conversion |
| 3 | Ten items with "some". Practise placing the X after shading |
| 4 | Ten "no conclusion follows" items: undistributed middle and two negatives |
| 5 | Three-premise chains |
| 6 | Twenty mixed items at 45 seconds each |
| 7 | Review every error and name the rule you broke |
Syllogisms are close cousins of conditional statements ("if ... then"), so it is worth practising both together; our guide to conditional logic questions uses the same elimination approach. For wider practice, try the mixed items in logical reasoning practice questions and the overview in deductive reasoning tests. If your target test is the Watson-Glaser, the deductions section works the same way, and you can practise it with the Watson-Glaser critical thinking test.
Frequently Asked Questions
Do I need to memorise all the valid syllogism forms?
No. Knowing four or five common forms helps you recognise easy items quickly, but the distribution rules and a quick Venn sketch let you judge any syllogism, including ones you have never seen.
Can Venn diagrams always solve syllogisms?
For categorical syllogisms with three terms, yes. Shade the regions a universal premise empties, mark an X where a particular premise says something exists, and read off what the conclusion needs. If the X could sit on either side of a line, the conclusion does not follow.
What if the syllogism has more than two premises?
Chain them. Combine two premises that share a term into an intermediate conclusion, then combine that with the next premise. Start with the premises that contain “some”, because they tell you where something definitely exists.
Does it matter whether the premises are true in real life?
No. A syllogism question tests validity, not truth. “All fish can fly. All salmon are fish. So all salmon can fly” is valid. Judge only whether the conclusion is forced by the premises as written.
Which tests include syllogism questions?
They appear in many deductive and logical reasoning tests used in graduate recruitment, in the deductions section of the Watson-Glaser critical thinking test, and in civil service and banking entrance exams in several countries.