How to solve syllogisms
Syllogisms: circles, not intuition
Draw the categories as circles, test each conclusion against every drawing the premises allow, and never let world knowledge vote.
Updated
'All bloravs are crintels. Some crintels are morvats.' The words are nonsense on purpose — syllogisms test whether you can follow structure while ignoring plausibility. The only reliable tool is the set diagram: circles inside, outside, or overlapping circles.
Encode each premise
'All A are B' → draw circle A entirely inside B. 'No A are B' → separate circles. 'Some A are B' → overlapping circles with a mark in the overlap. 'Some A are not B' → a mark in A outside B. The marks matter: 'some' guarantees at least one individual there.
MUST means: true in every allowed drawing
A conclusion follows only if it holds in every diagram consistent with the premises. To kill a conclusion, find ONE allowed drawing where it fails. Test each option by attempting to draw its counterexample — if you can, it doesn't follow.
The classic invalid moves
From 'All A are B', nothing follows about B being A (conversion error). From 'Some A are B', nothing follows about ALL of anything. Two 'some' premises never force a 'some' conclusion between the outer terms. When no option survives, 'none of these follows' is the answer — it appears precisely because solvers hate choosing it.
Five instant validity checks
Formal logic gives five rules that reject bad syllogisms before you draw anything. (1) Two negative premises ('no…', 'some…not') → nothing follows. (2) One negative premise → the conclusion must be negative; no negative premise → it can't be. (3) Two 'some' premises → nothing follows. (4) The middle term — the one appearing in both premises — must be taken universally ('all M…' or 'no…M') at least once; otherwise nothing follows. (5) A conclusion about all of a term needs a premise about all of it. Run these in seconds; the circles then only adjudicate the survivors.
The strategy
- Draw the premises. Nonsense words become circle labels — never translate them into real things.
- For each option, hunt for a counter-drawing. One counterexample kills it.
- Survivor found? Verify it holds in the extreme drawings too (circles barely overlapping, circles coinciding).
- Trust the diagram over the feeling of 'sounds right' — that feeling is exactly what the test is baiting.
Common traps
- Converting 'All A are B' into 'All B are A'.
- Existential slips: concluding 'some' from two 'all' premises about possibly-empty categories.
- Choosing a true-looking conclusion that is merely possible, not necessary.
Speed · ~70s/item: 60–90 seconds for two premises. The diagram is slower than intuition and right about 30% more often — the trade is spectacular.
Try it yourself: 4 practice questions
Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.
No flimets are trintels. All trintels are snavors. Which conclusion must be true?
Reveal the answer
The answer is D — No trintels are flimets..
Show why — the worked reasoning
All flurs are grelets. No grelets are grurels. Which conclusion must be true?
Reveal the answer
The answer is E — No flurs are grurels..
Show why — the worked reasoning
No grelets are grans. No grans are vrelels. Which conclusion must be true?
Reveal the answer
The answer is A — No grans are grelets..
Show why — the worked reasoning
All blims are flanels. All flanels are zmanets. Which conclusion must be true?
Reveal the answer
The answer is B — All blims are zmanets..
Show why — the worked reasoning
Try questions like this
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Questions people ask
What is a syllogism question?
Two or more statements, such as "All A are B" and "Some B are C", and a choice of conclusions. You pick the one that must be true if the statements are true.
Should you use real-world knowledge?
No. Judge only what the statements allow. A conclusion that sounds true but does not follow is the most common wrong answer, and many questions use nonsense words for this reason.
How long should a syllogism take?
About 60 to 90 seconds for two statements. Drawing the categories as circles is slower than intuition and right far more often.
Will syllogisms questions be on the free test?
Maybe. The free test gives verbal & logic 5 of its 20 questions, spread across 11 different question types, so any one test may or may not include this kind.