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Some of ProofQuest’s cast are still learning. When you teach them, YOU learn it best — catch what they get wrong, then quiz them.
Teach Direct-Proof Dora
You be the teacher — Direct-Proof Dora is still learning. Helping Direct-Proof Dora figure it out is the practice. (Direct-Proof Dora's progress stays on this device; nothing is sent anywhere.)
🎓 In a minute you'll be the teacher. Get ready to teach Direct-Proof Dora: direct proof.
A direct proof starts from the premises and reasons step by step to the claim. Examples can suggest a rule but can't prove it for every case.
You've helped them one at a time. The real understanding is how the ideas CONNECT — teach that next.
Contradiction Cassius (proof by contradiction) ×Contrapositive Cara (proof by contrapositive)
Both Cassius and Cara begin by assuming something is NOT true. What do they share?
Contradiction Cassius then says: “Contradiction and contrapositive are just two names for the same proof — always interchangeable.” — is that right?
The link: both are "argue from the negation" techniques — Cara flips the implication, Cassius blows it up.
Two ways to work backwards from "suppose it's false."
Induction Ida (standard induction (assume case n)) ×Strong-Induction Sten (strong induction (assume all cases ≤ n))
Ida and Sten both use a base case and a step. What's the ONE difference?
Induction Ida then says: “Strong induction doesn't need a base case — it assumes everything already.” — is that right?
The link: same base-case-plus-step skeleton — Sten just gets to lean on ALL the earlier rungs, not only the last one.
One ladder, two grips.
Capstone — three claims, three provers
A worksheet has three very different claims. Each needs a DIFFERENT kind of proof — bring in the right cast member for each.
"There EXISTS an even number that is the sum of two primes." (show one)
Who do you bring in?
"1 + 2 + … + n = n(n+1)/2 for EVERY positive n." (a pattern that never ends)
Who do you bring in?
"ALL prime numbers are odd." (a sweeping claim you doubt)
Who do you bring in?
The synthesis: existence wanted a construction, a never-ending pattern wanted induction, and a sweeping false claim fell to one counterexample — the CLAIM tells you which prover to call.
A proof isn't one tool — it's choosing the right one for the shape of the claim.
