Logic True or False Quiz: 10 Statements to Judge

This logic true or false quiz gives you ten statements about shapes, numbers, groups and arguments, and asks whether each one is true, false or cannot be determined from the facts, with famous surprises such as zero being even and 0.999 repeating equaling 1, plus a look at George Boole and Kurt Gödel. Judge each statement carefully.

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

Question 1 / 10 Time: 90s

Shapes
True or false: All squares are rectangles.
Groups
True or false: If all A are B, then all B are A.
Numbers
True or false: Zero is an even number.
Logic
True or false: A statement and its contrapositive always have the same truth value.
Primes
True or false: Every prime number is odd.
Categories
No cats bark. Tom barks. True or false: Tom is not a cat.
Some
Some people in the room are tall. True or false: some people in the room are not tall.
Numbers
True or false: The sum of two odd numbers is always even.
Decimals
True or false: 0.999 repeating forever is exactly equal to 1.
Order
Anna is older than Ben, and Ben is older than Cat. True or false: Cat is older than Anna.

Explanations: answer key for all 10 questions

Q1: True or false: All squares are rectangles.
Answer: True
A rectangle is any four-sided shape with four right angles. Squares have four right angles too, with the extra feature of equal sides.
Q2: True or false: If all A are B, then all B are A.
Answer: False
All dogs are animals, but not all animals are dogs. Reversing an all statement is a common mistake.
Q3: True or false: Zero is an even number.
Answer: True
A number is even if it can be divided by 2 with no remainder. Zero divided by 2 is zero, so zero is even.
Q4: True or false: A statement and its contrapositive always have the same truth value.
Answer: True
If P then Q and if not Q then not P are logically equivalent. If one is true, the other is true as well.
Q5: True or false: Every prime number is odd.
Answer: False
The number 2 is prime because it can be divided only by 1 and itself, and it is even. It is the only even prime.
Q6: No cats bark. Tom barks. True or false: Tom is not a cat.
Answer: True
If Tom were a cat, he could not bark. Since he barks, he cannot be a cat.
Q7: Some people in the room are tall. True or false: some people in the room are not tall.
Answer: Cannot be determined
In logic, some means at least one, and it does not rule out all. Everyone in the room might be tall, so we cannot be sure.
Q8: True or false: The sum of two odd numbers is always even.
Answer: True
Each odd number is one more than an even number, so the two extra ones make another even pair. For example, 3 plus 5 is 8.
Q9: True or false: 0.999 repeating forever is exactly equal to 1.
Answer: True
One third is 0.333 repeating, and three thirds make 1, which is 0.999 repeating. They are two ways of writing the same number.
Q10: Anna is older than Ben, and Ben is older than Cat. True or false: Cat is older than Anna.
Answer: False
If Anna is older than Ben and Ben is older than Cat, Anna is older than Cat. Being older than is a transitive relation.

Logic True or False Quiz – Judging Statements

True or false questions look simple, but in logic they hide many surprises. Some statements are definitely true, some are definitely false and some cannot be decided from the information given. Learning to tell these apart is an important part of reasoning, especially in exams, debates and everyday decisions.

In the 19th century, the English mathematician George Boole created an algebra of true and false values, now called Boolean logic. It treats statements like numbers that can be combined with and, or and not. More than a hundred years later, Boolean logic became the foundation of digital computers, which process information as ones and zeros.

Some true statements surprise people. Zero is even, because it divides by 2 with no remainder. The number 2 is the only even prime. And 0.999 repeating forever equals exactly 1, a fact that has started countless online arguments. These examples show why careful definitions matter in logic and math.

Other questions test how we read words like all and some. If all A are B, it does not follow that all B are A. And in logic, some only means at least one, so it does not tell us whether some are not.

In 1931, the Austrian logician Kurt Gödel proved that in any consistent system of arithmetic, there are true statements that can never be proven within it. His incompleteness theorems changed mathematics and philosophy.

Practicing true or false logic builds precision, helps you avoid hasty conclusions and makes you a sharper reader.

What This Quiz Teaches

This quiz is perfect for students, math fans and logic lovers.

How to judge true, false and undecided statements
Why all A are B cannot be reversed
Why zero is even and 2 is the only even prime
Why 0.999 repeating equals 1
Transitive relations like older than
George Boole and Kurt Gödel

Quick Facts About Logic

George Boole was largely self-taught in mathematics.
Computers store true and false as 1 and 0.
Kurt Gödel published his incompleteness theorems at age 25.
Many standardized tests include true, false and cannot say questions.
Logic gates in computer chips perform and, or and not operations.
A tautology is a statement that is always true.