Week 4 — Requirement or Guarantee: Reading Rules Built on If

Assignment 4 of the term — rewrite each rule as "if, then", tell what it requires from what it guarantees, test the reasoning built on it, and explain the difference to someone new to the subject.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, evidence-based evaluation. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. In Week 3 you learned to test an argument with the counterexample method; this week you read rules built on "if" exactly as they are written and test the forms people build on them. This week's lecture tutorial, quiz, discussion, and Argument Workshop practise the same ideas from other angles; this assignment is where you put them together on two short texts.

The task

Your first text is an illustrative course-registration notice, with no real school behind it: "You can register for the advanced writing course only if you passed the introductory writing course. The advanced course has 3 sections of 32 seats each, and 120 students who passed the introductory course tried to register for it."

Your second text is an illustrative store policy, with no real store behind it: "Full refunds are given only if the item is returned within 30 days." Below the policy, a store log reads: "Of the last 40 items returned within 30 days, 34 received a full refund." A customer reasons: "I returned my blender within 30 days, so I will get a full refund."

Work these four problems, showing your arithmetic and quoting the sentences you use:

1. The registration notice says the advanced course has 3 sections of 32 seats each. How many seats does the advanced course have in all?
2. Using the seat total from Problem 1, how many of the 120 students who passed the introductory course and tried to register could not get a seat?
3. The store log says 34 of the last 40 items returned within 30 days received a full refund. What percentage of those returns received a full refund?
4. Of the same 40 logged returns, how many did not receive a full refund?

Beside each answer, add one brief interpretation:

• Problem 1: rewrite the notice's first sentence as an "if, then" sentence, say which condition it makes necessary, and explain why passing the introductory course is not sufficient by describing one student who passed but cannot register.
• Problem 2: write the converse of your rewritten sentence, explain why the students who could not get a seat show the converse is false while the notice stays true, and write the contrapositive.
• Problem 3: rewrite the refund policy as an "if, then" sentence, then name the form of the customer's reasoning and say whether it is valid.
• Problem 4: explain why the returns that did not receive a full refund are counterexamples to the customer's form, then write the message to the customer's friend described below.

Explain it to a non-expert

The customer's friend has never studied logic and asks, "Almost every return within 30 days got its money back. Doesn't returning it in time guarantee the refund?" Write a 3–5 sentence message that explains in everyday words the difference between a requirement and a guarantee, reports the percentage you found and how many returns did not get a full refund, and names one limit: the policy says what a refund requires, not everything it requires. Explain any technical term in everyday words. More than one good answer is possible.

For a different, ungraded example, imagine a gym that posts "You can book a court only if you have paid this month's dues." Model answer: "Paying your dues is a requirement, not a ticket. The rule says nobody books a court without paying, but it never promises that paying gets you a court. If every court is taken, a member who paid still waits, and the rule has not been broken."

Use that pattern for the friend, with your own wording and evidence.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to the friend before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show calculations and quote the sentences you use when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the work for you. If it calls the customer's reasoning valid because most returns were refunded, or treats passing the introductory course as a guarantee of a seat, say so and ask it why.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach for an introductory critical thinking course. Draw out and challenge MY thinking about rewriting "only if" as "if, then", telling a necessary condition from a sufficient one, telling a conditional from its converse and contrapositive, and naming and testing the forms built on a conditional. Do not write my assignment for me, do not invent work I did not show, never invent a statistic, a study, or a quotation, never name a real person, school, company, or store, and never use logic symbols. Do not name any informal fallacy.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The texts: an illustrative course-registration notice, "You can register for the advanced writing course only if you passed the introductory writing course. The advanced course has 3 sections of 32 seats each, and 120 students who passed the introductory course tried to register for it." And an illustrative store policy, "Full refunds are given only if the item is returned within 30 days." A store log reads: "Of the last 40 items returned within 30 days, 34 received a full refund." A customer reasons: "I returned my blender within 30 days, so I will get a full refund."
PROBLEM P1: The registration notice says the advanced course has 3 sections of 32 seats each. How many seats does the advanced course have in all?
PROBLEM P2: Using the seat total from Problem 1, how many of the 120 students who passed the introductory course and tried to register could not get a seat?
PROBLEM P3: The store log says 34 of the last 40 items returned within 30 days received a full refund. What percentage of those returns received a full refund?
PROBLEM P4: Of the same 40 logged returns, how many did not receive a full refund?
After the four answers, I must briefly interpret each one: for P1, rewrite the notice's first sentence as "if, then", say which condition it makes necessary, and describe a student who passed but cannot register to show passing is not sufficient; for P2, write the converse, explain why the students without a seat show the converse is false while the notice stays true, and write the contrapositive; for P3, rewrite the refund policy as "if, then", name the form of the customer's reasoning, and say whether it is valid; for P4, explain why the returns without a full refund are counterexamples to the customer's form. I must then write a 3-5 sentence message to the customer's friend explaining the difference between a requirement and a guarantee, reporting the percentage and the number of returns without a full refund, and naming one limit. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: correct computations (20 points), argument evaluation (48 points), clarity for a non-expert reader (16 points), and showing the evidence so it can be checked (16 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 2.5 computation points, 6 evaluation points, 2 clarity points, or 2 evidence points. Sum all four problems within each criterion. Count my friend message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct seat total, count, or percentage = 2; the right values and operation with only an arithmetic slip = 1; a missing answer or the wrong values or operation = 0. Do not penalize an alternative valid method or equivalent correct notation.
EVALUATION UNITS: For P1-P3 separately, an interpretation that meets both parts named for that problem = 2; exactly one part = 1; neither = 0. For P4, BOTH an explanation of why the returns without a full refund are counterexamples to the customer's form AND a friend message that explains requirement versus guarantee, reports the percentage and the count, and names a limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate evaluation = 0; naming a term alone does not earn a unit, and calling affirming the consequent valid is not accurate. An arithmetic slip alone is not an evaluation error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to critical thinking, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the friend message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
EVIDENCE UNITS: For each problem, checkable values and steps, with every quoted sentence matching the notice, the policy, or the log as printed = 2; a relevant but incomplete value, step, or quotation, or a quotation that drifts from the text = 1; an answer alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my message to the friend AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned total; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the total for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations, quotations, and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised work, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised work with all four answers, their brief interpretations, and your message to the friend — written, or recorded as audio or video with a transcript, or as a labelled sketch that sets each rule beside its "if, then" rewrite with the necessary and sufficient conditions marked and a short note that says it in words; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 4 skills — rewriting "only if" as "if, then", telling a necessary condition from a sufficient one, telling a conditional from its converse and contrapositive, naming and testing the form of an argument built on a conditional, and explaining the difference to someone new — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message to the friend. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and check every quoted sentence against the notice, the policy, and the log as printed. Write a second draft and add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised work, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce, and check any sentence it quotes against the notice, the policy, and the log as printed here. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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