Module 1: Proof Techniques & Discrete Structures: Mistake Clinic

This clinic turns wrong moves into reusable judgment. Use it after each practice page and again before the quiz or checkpoint.

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Module-Specific Mistake Radar

Start with these traps. Replace or extend them with real mistakes from your own work.

Mistake to look for	Where it shows up	Symptom	Repair evidence
Finishing Logic and Proof Method Diagnostics with only a final answer	Logic and Proof Method Diagnostics	The work has no failed case, trace, test, proof gap, or design stress point.	Add the smallest broken example and show the repair that changes the result.
Finishing Sets, Functions, and Relations Lab with only a final answer	Sets, Functions, and Relations Lab	The work has no failed case, trace, test, proof gap, or design stress point.	Add the smallest broken example and show the repair that changes the result.
Finishing Induction and Recursion Clinic with only a final answer	Induction and Recursion Clinic	The work has no failed case, trace, test, proof gap, or design stress point.	Add the smallest broken example and show the repair that changes the result.
Finishing Code Katas with only a final answer	Code Katas	The work has no failed case, trace, test, proof gap, or design stress point.	Add the smallest broken example and show the repair that changes the result.
Treating Propositions, Implication, and Equivalence as vocabulary instead of a tool	Propositions, Implication, and Equivalence	The explanation names the concept but cannot decide between two cases.	Write one example, one non-example, and the rule that separates them.
Treating Truth Tables, Validity, and Equivalence as vocabulary instead of a tool	Truth Tables, Validity, and Equivalence	The explanation names the concept but cannot decide between two cases.	Write one example, one non-example, and the rule that separates them.

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Practice Mistake Checks

Pull any miss from these checks into your mistake log.

Logic and Proof Method Diagnostics

Source: practice/01-logic-and-proof-method-diagnostics.md

For each statement below, identify the error:

1. "The negation of for all x P(x) is for all x not P(x)."
2. "I proved Q -> P, so P -> Q is done."
3. "I checked the statement for n = 1, 2, 3, 4, so it must be true for all n."
4. "I used contradiction because I was not sure what else to do."

Sets, Functions, and Relations Lab

Source: practice/02-sets-functions-and-relations-lab.md

Diagnose the flaw in each claim:

1. "Because {1} in P({1,2}), therefore {1} subseteq P({1,2})."
2. "The function f(x) = x^2 on the reals is bijective because every input has one output."
3. "A relation is antisymmetric exactly when it is not symmetric."
4. "To prove two sets are equal, it is enough to show the left side is contained in the right side."

Induction and Recursion Clinic

Source: practice/03-induction-proof-clinic.md

Find the flaw in each move:

1. "Assume P(n + 1) and prove P(n + 1)."
2. "The base case is obvious, so I skipped it."
3. "In the inductive step, I used the theorem for all smaller values even though I set up ordinary induction."
4. "I used induction on string length even though the recursive constructors were easier to follow directly."

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Repair Protocol

For each real mistake:

1. Reproduce the failure on the smallest example, trace, proof, query, command, or design sketch.
2. Name the hidden assumption.
3. Repair the artifact.
4. Save evidence that changed: failing then passing test, corrected proof step, revised diagram, safer command, benchmark, or review note.
5. Add one retrieval card beginning with Check... before... or Do not use... when....

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Mistake Log

Date	Mistake	Symptom	Root cause	Repair evidence	Retrieval card
Starter	Pick one radar row above	Explain how it would fail in this module	Name the assumption	Add a counterexample or corrected artifact	Write the card before closing the page

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Completion Standard

• At least five real mistakes are logged.
• At least two mistakes include a counterexample or failing test.
• At least one mistake connects to an older semester skill.
• At least one correction changes code, a proof, a diagram, a command transcript, a query, or a design decision.