Week 4 — Requirement or Guarantee: Reading Rules Built on If — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

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 week you learned to read a conditional exactly as it is written, to rewrite "only if" as "if, then", to tell a necessary condition from a sufficient one, to tell a conditional from its converse and contrapositive, and to name and test the forms built on a conditional. In this assignment you work four short problems on two illustrative texts, interpret each one, and explain the difference between a requirement and a guarantee to someone who has never studied critical thinking. This week's lecture tutorial, quiz, discussion, and Argument Workshop practise the same ideas from other angles.

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.

Show your arithmetic and quote the sentences you use. A reader should be able to reproduce every number you report, and find every quoted sentence in the notice, the policy, or the log, without guessing which values, steps, or sentences you used.

Deliverables

Submit a single report containing:

• the four answers, each with the arithmetic shown and the brief interpretation the task names for that problem;
• your message to the friend, explaining the difference between a requirement and a guarantee, reporting the percentage and how many returns did not get a full refund, and naming one limit; and
• a one-line restatement of the values you used (the sections and seats, the students who tried to register, and the logged and refunded returns), so your answers are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes 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. 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.

How you'll be graded

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

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without a chatbot or other AI tool. Quote the notice, the policy, and the log only as they are printed here, word for word. Submitting AI-generated work as your own, or copying another student's work, is an integrity violation under the course policy.

Built with The Course Maker · samples.thecoursemaker.com