All squares are rectangles. All rectangles have four sides. What follows?

All four-sided shapes are squares

Some rectangles are not squares

Some birds cannot fly. All penguins are birds. What follows from these two statements alone?

Nothing about penguins flying follows

No vegetables are sweets. Some sweets are healthy. Which statement must be true?

Some healthy things are not vegetables

When do logicians call an argument valid?

When its conclusion must be true whenever its premises are true

When its premises are about real things

Syllogism Quiz: 10 Arguments to Test If the Logic Holds

This syllogism quiz asks you to decide which conclusions really follow from two starting statements, using all, some and none, with made-up words, animals and shapes, the famous Socrates example from Aristotle and the diagram methods of John Venn and Lewis Carroll. Ten questions, and each one tests whether the logic truly holds.

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🎯 Daily Trivia Challenge • 🧠 10 Questions • ⏱️ 90 Seconds

Question 1 / 10 Time: 90s

Some
All poets are dreamers. Some dreamers are teachers. Must some poets be teachers?
All
All squares are rectangles. All rectangles have four sides. What follows?
None
No reptiles have fur. All snakes are reptiles. What follows?
Some
Some birds cannot fly. All penguins are birds. What follows from these two statements alone?
Made-up words
All glorps are fleps. No fleps are zibs. What follows?
History
Which ancient Greek philosopher first studied syllogisms in a systematic way?
Pets
All cats have tails. My pet has a tail. What follows?
Some
Some students are athletes. All athletes are early risers. What follows?
None
No vegetables are sweets. Some sweets are healthy. Which statement must be true?
Validity
When do logicians call an argument valid?

Explanations: answer key for all 10 questions

Q1: All poets are dreamers. Some dreamers are teachers. Must some poets be teachers?
Answer: No, not necessarily
The teachers who are dreamers might not be poets at all. Two groups that share a third group do not have to overlap with each other.
Q2: All squares are rectangles. All rectangles have four sides. What follows?
Answer: All squares have four sides
If every square is a rectangle and every rectangle has four sides, then every square has four sides. This is the simplest valid syllogism.
Q3: No reptiles have fur. All snakes are reptiles. What follows?
Answer: No snakes have fur
Every snake belongs to the reptiles, and no reptile has fur, so no snake can have fur. The conclusion is forced by the premises.
Q4: Some birds cannot fly. All penguins are birds. What follows from these two statements alone?
Answer: Nothing about penguins flying follows
The birds that cannot fly might be other birds, such as ostriches. In real life penguins cannot fly, but these premises do not prove it.
Q5: All glorps are fleps. No fleps are zibs. What follows?
Answer: No glorps are zibs
Every glorp is inside the group of fleps, and that group shares nothing with zibs. Made-up words help you judge the logic without being distracted by real-world facts.
Q6: Which ancient Greek philosopher first studied syllogisms in a systematic way?
Answer: Aristotle
Aristotle described syllogisms in his work Prior Analytics. His system of logic was taught in Europe and the Islamic world for about 2,000 years.
Q7: All cats have tails. My pet has a tail. What follows?
Answer: My pet may or may not be a cat
Many animals besides cats have tails, such as dogs. Concluding that the pet is a cat is a classic error called the undistributed middle.
Q8: Some students are athletes. All athletes are early risers. What follows?
Answer: Some students are early risers
The students who are athletes must also be early risers. We know nothing about the other students, so we can only say some.
Q9: No vegetables are sweets. Some sweets are healthy. Which statement must be true?
Answer: Some healthy things are not vegetables
The healthy sweets cannot be vegetables, because no sweets are vegetables. So at least some healthy things are not vegetables.
Q10: When do logicians call an argument valid?
Answer: When its conclusion must be true whenever its premises are true
Validity is about the structure of an argument. A valid argument with false premises can still have a false conclusion.

Syllogism Quiz – The Logic of All, Some and None

A syllogism is an argument with two starting statements, called premises, and one conclusion. A classic example is: all humans are mortal, Socrates is a human, so Socrates is mortal. Syllogisms use words such as all, some and none to describe how groups relate to each other. Learning to judge them is a core skill in logic and critical thinking.

The ancient Greek philosopher Aristotle was the first to study syllogisms in a systematic way, in his work Prior Analytics. He listed which patterns are valid and which are not. For about 2,000 years, his system was a central part of education in Europe and the Islamic world, and medieval students even learned Latin nicknames for each valid pattern.

A key idea is that validity is about structure, not truth. A valid argument guarantees a true conclusion only when its premises are true. That is why this quiz uses made-up words such as glorps and fleps: they force you to judge the logic itself, without relying on what you already know about the world.

The most common mistakes involve the word some and shared groups. If all cats have tails and your pet has a tail, the pet could still be a dog. If some birds cannot fly, that does not tell you which birds. Logicians call these errors fallacies.

Diagrams make syllogisms much easier. In the 1880s, John Venn introduced overlapping circles to show groups, and Lewis Carroll created his own diagram method for logic puzzles. Drawing the groups often reveals the answer at once.

Practicing syllogisms sharpens your reading and makes it easier to spot weak arguments in daily life.

What This Quiz Teaches

This quiz is perfect for logic fans, students and test takers.

What a syllogism is
Valid conclusions with all, some and none
Why made-up words help test logic
The undistributed middle and other errors
Aristotle and the history of logic
Venn diagrams and Lewis Carroll's method

Quick Facts About Syllogisms

John Venn introduced his diagrams in 1880.
Medieval students memorized valid patterns with names like Barbara and Celarent.
Lewis Carroll published The Game of Logic in 1886.
Syllogism questions appear in many aptitude tests.
A sound argument is one that is valid and has true premises.
Modern logic expanded Aristotle's system with symbols and variables.