Logic Exercises

Multiple choice, truth table completion, simplification, equivalence checks, expression input and expression evaluation, and proofs — including proof completion and a drag-and-drop proof builder. They are grouped into propositional logic, Boolean algebra, truth tables, logical equivalence, predicate logic and natural deduction, and you can filter by category, type, difficulty and tag.

What do the difficulty levels mean?

There are four: beginner, intermediate, advanced and expert. They describe how much you need to know rather than how long the exercise takes; each exercise also shows an estimated time and the points it is worth.

What is a training session?

A run of exercises at one difficulty, optionally narrowed to the categories and types you want to work on. It keeps score as you go, and at the end it summarises how you did and offers the next difficulty up when there is one.

How are my answers checked?

In your browser, by the same engine that powers the calculator. Most exercise types compare your answer with the expected one after normalising spacing and notation; expression input goes further and checks logical equivalence, so a formula written differently but meaning the same thing still counts as correct. Every exercise carries an explanation, shown once you have answered.

Can I get a hint if I am stuck?

Yes, where an exercise has one: a hint you can reveal without giving the answer away. If it is not enough, the guide covering that topic is usually the faster way back in — the exercise categories and the guides use the same topics.

See all questions

Training

What is the result of: true AND false?

What is the result of: false OR true?

What is the result of: NOT true?

Arrange the following steps in the correct order to prove Q from the given premises. Goal: Prove Q

Evaluate the following expression: P ∧ Q when P = true and Q = true

Evaluate the following expression: P ∨ Q when P = false and Q = true

Fill in the missing justifications for this proof. Goal: Prove Q

Express the following statement using logical symbols: "If it rains, then the ground is wet" Use: - R for "it rains" - W for "the ground is wet" - ** → ** for implication Enter your answer using the symbols available in the calculator.

Express the following statement using logical symbols: "It is sunny and warm" Use: - S for "it is sunny" - W for "it is warm" - ** ∧ ** for conjunction (and) Enter your answer using the symbols available in the calculator.

Express the following statement using logical symbols: "I will study math or physics" Use: - M for "I will study math" - P for "I will study physics" - ** ∨ ** for disjunction (or) Enter your answer using the symbols available in the calculator.

Express the following statement using logical symbols: "It is not raining" Use: - R for "it is raining" - ¬ for negation (not) Enter your answer using the symbols available in the calculator.

Express the following statement using logical symbols: "The alarm rings if and only if motion is detected" Use: - A for "the alarm rings" - M for "motion is detected" - ** ↔ ** for biconditional (if and only if) Enter your answer using the symbols available in the calculator.

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Boolean Algebra

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Multiple Choice

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Drag & Drop Proof

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Expression Input

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Frequently Asked Questions

Express the following statement using logical symbols: "If it rains, then the ground is wet" Use: - R for "it rains" - W for "the ground is wet" - → for implication Enter your answer using the symbols available in the calculator.

Express the following statement using logical symbols: "It is sunny and warm" Use: - S for "it is sunny" - W for "it is warm" - ∧ for conjunction (and) Enter your answer using the symbols available in the calculator.

Express the following statement using logical symbols: "I will study math or physics" Use: - M for "I will study math" - P for "I will study physics" - ∨ for disjunction (or) Enter your answer using the symbols available in the calculator.

Express the following statement using logical symbols: "The alarm rings if and only if motion is detected" Use: - A for "the alarm rings" - M for "motion is detected" - ↔ for biconditional (if and only if) Enter your answer using the symbols available in the calculator.