Practise syllogisms and logical conclusions: Vienna entrance test
Syllogisms, called Schlussfolgerungen (logical conclusions) in the official worksheet, are part of the cognitive block of the Informatics entrance test at TU Wien and Uni Wien. You get two statements (premises) and must decide which conclusion necessarily follows.
The key: you may only reason from what the premises say, never from your general knowledge. That makes the rules strict and learnable. This page explains them, and you can drill them free on VWUPass without signing up.
Practise syllogisms freeWhat is a syllogism?
A syllogism has two premises and a candidate conclusion. Your job is not to check whether the statements are true, but whether the conclusion necessarily follows once you take the premises as given.
Necessarily means: there must be no conceivable case in which both premises hold and the conclusion is still false. A single counterexample is enough to reject the conclusion.
- Premise 1 and premise 2: the given statements
- Conclusion: the candidate inference to check
- What is tested is validity, not real-world truth
- One counterexample is enough to overturn the conclusion
The quantifiers: all, some, none
Almost all syllogisms hinge on four quantifiers: all (every), no (not a single one), some (at least one), and some not. Two rules of thumb solve most items.
First: if at least one premise is particular, that is uses some, then the conclusion can only be particular. A some premise never yields an all. Second: if at least one premise is negative (no, not), then the conclusion must be negative too. Two negative premises usually yield nothing valid at all.
- all A are B: every A is a B, but not every B need be an A
- no A are B: A and B share no case
- some A are B: at least one A is a B, and it says nothing about the rest
- a particular premise (some) forces a particular conclusion
- a negative premise forces a negative conclusion
Why at least matters so much
The word at least (at least one) carries a strict logical meaning in the test. Some means exactly at least one and leaves open whether it might be all. So it does not rule all out, but it does not claim it either.
This creates a trap: from some A are B you may not infer that some A are not B. Perhaps all A are B after all. The reverse does hold, though: from all A are B it follows that some A are B, because if all of them are, at least one is (as long as an A exists at all).
Treating absurd premises as true
Some premises contradict reality, for example all cats can fly. That is deliberate. You are meant to switch off your world knowledge and reason purely from what is given.
So accept the premise as true, however absurd it sounds, and then check whether the conclusion necessarily follows. Falling back on everyday knowledge costs points even when the logic is clear-cut.
Premise 1: All programmers drink coffee. Premise 2: Some coffee drinkers are early risers. Conclusion: Some programmers are early risers. Valid or not?
- Premise 1 says: all programmers sit inside the group of coffee drinkers.
- Premise 2 says: at least one coffee drinker is an early riser. Which coffee drinker stays open.
- Counterexample: the early-rising coffee drinkers could all be non-programmers, since plenty of other people drink coffee too.
- Because both premises can be true while the conclusion is false, it does not follow necessarily.
Answer:Not valid. The overlap from premise 2 need not fall among the programmers, a classic fallacy built on a some premise.
A step-by-step approach
A fixed procedure saves time in the test and stops you from guessing by gut feeling. The fastest check is to hunt for a counterexample: if you find one, the conclusion is invalid; if you cannot, it follows necessarily.
If you think visually, draw the groups as circles (set diagrams): all as a circle inside a circle, no as separate circles, some as overlapping circles. Whatever holds in every allowed drawing follows necessarily.
- Mark the quantifiers: all, no, some, some not
- Check the rules: particular forces particular, negative forces negative
- Look for a counterexample, using a set diagram if needed
- Ignore world knowledge, even with absurd premises
Frequently asked questions
What is the difference between syllogisms and Schlussfolgerungen?
None in substance. Schlussfolgerungen is the wording in the official worksheet, and syllogism is the classic technical term for exactly these two-premise, one-conclusion tasks. They mean the same thing.
What exactly does at least mean in syllogisms?
At least one means one or more, with no upper bound. It does not rule out that it is even all of them. That is why some A are B does not imply that some A are not B.
Do I need to watch out for absurd or false premises?
Yes, but not the way you might think. Absurd premises are added on purpose. You treat them as true and reason purely logically. Your everyday knowledge must never sway the answer.
Can anything follow from two some premises?
As a rule, no. When both premises only say some, there is almost always a counterexample that arranges the groups differently. Such items are usually invalid, but still verify with a counterexample.
How can I practise syllogisms for the Vienna entrance test?
Best with many items under time pressure in the test format. On VWUPass you can practise syllogisms free and without signing up, with an explanation after each item.