Introduction to Mathematical Proof: Worksheet

Introduction to Mathematical Proof: Worksheet

Complete this original worksheet without protected answer keys, then verify reasoning with course-approved sources. Teaches definitions, logic, direct and indirect proof, induction, and construction of rigorous arguments. Course titles, local sequences, grading, safety rules, required tools, and assessment formats vary; align this resource with the current syllabus and instructor directions.

Learning outcomes

• Explain and apply definitions and quantifiers, then connect it to direct proof using course-appropriate evidence.
• Explain and apply direct proof, then connect it to contrapositive and contradiction using course-appropriate evidence.
• Explain and apply contrapositive and contradiction, then connect it to mathematical induction using course-appropriate evidence.
• Explain and apply mathematical induction, then connect it to counterexamples using course-appropriate evidence.
• Explain and apply counterexamples, then connect it to definitions and quantifiers using course-appropriate evidence.

Prerequisite readiness

algebra, set notation, functions, and careful reading of definitions Use a short ungraded check, repair the smallest missing skill, and immediately retest it in a course-level task.

Original worksheet prompts

1. Explain definitions and quantifiers and connect it to the course purpose.
2. Apply definitions and quantifiers to a new example; show a check and one limitation.
3. Explain direct proof and connect it to the course purpose.
4. Apply direct proof to a new example; show a check and one limitation.
5. Explain contrapositive and contradiction and connect it to the course purpose.
6. Apply contrapositive and contradiction to a new example; show a check and one limitation.
7. Explain mathematical induction and connect it to the course purpose.
8. Apply mathematical induction to a new example; show a check and one limitation.
9. Explain counterexamples and connect it to the course purpose.
10. Apply counterexamples to a new example; show a check and one limitation.

Self-review

Compare each response with instructor criteria. Correct the first unsupported move and retry one changed-condition prompt.

Reliable method

unpack the statement, identify quantifiers, test examples, choose a proof structure, justify each implication, and edit for completeness Keep assumptions, intermediate reasoning, units, sources, tool use, and checks visible so another learner can follow the decision process.

Representative application

Prove a divisibility statement and explain why checking many integers is useful exploration but not proof. Predict a reasonable result before working, compare the outcome with the prediction, and explain limitations or alternative interpretations.

Error recovery

Watch for starting algebra before stating assumptions or using the desired conclusion as an intermediate fact. Mark the first unsupported move, classify the cause, correct the reasoning, and schedule a fresh mixed recheck after a delay.

Accessibility, integrity, and safety

Use approved accommodations and accessible formats. Follow course rules for collaboration, citation, calculators, software, generative tools, laboratories, clinical settings, field activity, privacy, copyright, and human or animal subjects. Never use Exams.fit to obtain protected questions or bypass assessment rules.

Evidence to save

When permitted, preserve a polished proof with definitions, logical structure, edge cases, and revision notes with the prompt, first attempt, feedback, revision, verification, and reflection. Remove restricted assessment content and private or proprietary information.

Open-learning reference

Compare this original Exams.fit resource with the relevant OpenStax collection and MIT OpenCourseWare when they match the local course. Reviewed August 2, 2026. This page does not replace the current syllabus, instructor, institution, or qualified professional.