Visualize logical derivations
Apply rules one at a time
Verify each logical step
Master inference rules
Select a theorem and click "Start Proof" to see the step-by-step derivation
Click "Start Proof" to begin the logical derivation.
Complete the proof to see the summary.
Each step should follow directly from previous statements using valid inference rules.
1. Assume n is even
2. Then n = 2k for some integer k
3. n² = (2k)² = 4k² = 2(2k²)
4. 2k² is an integer
5. Therefore n² is even �?/code>Don't assume what you're trying to prove!
// WRONG: Proving A by assuming A
1. Assume P is true
2. If P then P (trivially true)
3. Therefore P is true
// This proves nothing!Use contradiction when direct proof is difficult or when proving something doesn't exist. Assume the negation, derive a contradiction, and conclude the original statement is true.
Induction proves statements for all natural numbers: prove the base case (n=1), then prove if true for n, it's true for n+1. Like climbing a ladder - if you can get on step 1 and always climb to the next step, you can reach any step.
Direct proof is best for "if A then B" statements. Use induction for statements about all natural numbers. Contradiction works well for uniqueness/impossibility proofs. Contrapositive is useful when the negation is easier to work with.