Week 5 — Who Is In, Who Is Out: Testing Rules About Groups — Traditional alternative (no AI)

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

Assignment 5 of the term — rewrite each rule about groups into a categorical form, test the reasoning built on it with a Venn diagram described in words, and explain what a rule does not say to someone new to the subject.

This week you learned to read the four categorical forms, to rewrite everyday sentences into them, to name the three terms of a categorical syllogism, to test a syllogism with a three-circle Venn diagram described in words, and to read "some" as "at least one". In this assignment you work four short problems on two illustrative texts, interpret each one, and explain what a rule does not say 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 set of hiking-club rules, with no real club behind it: "Only members who have completed the safety course may lead a club hike. Every hike leader carries a two-way radio. The club has 4 teams of 15 members each, and 18 members have completed the safety course." A member reasons: "All hike leaders completed the safety course, and all hike leaders carry a radio, so everyone who carries a radio completed the safety course."

Your second text is an illustrative store policy, with no real store behind it: "No sale items are returnable items. Some clearance items are sale items." Below the policy, a store log reads: "Of the last 40 clearance items sold, 12 were sale items." A shopper reasons: "No sale items are returnable, and some clearance items are sale items, so some clearance items are not returnable."

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

1. The club rules say the club has 4 teams of 15 members each. How many members does the club have in all?
2. Using the member total from Problem 1, how many members have not completed the safety course?
3. The store log says 12 of the last 40 clearance items sold were sale items. What percentage of those clearance items were sale items?
4. Of the same 40 logged clearance items, how many were not sale items?

Beside each answer, add one brief interpretation:

• Problem 1: rewrite the club's first rule into one of the four categorical forms, name its subject term and predicate term, and say one thing the rule does not say.
• Problem 2: test the member's syllogism with a three-circle Venn diagram described in words, give the verdict, and describe a counterexample built from one of the members who have not completed the safety course.
• Problem 3: test the shopper's syllogism with a three-circle Venn diagram described in words, give the verdict, and name its middle term.
• Problem 4: explain whether the store policy tells you anything about whether the clearance items that were not sale items can be returned, then write the message to the shopper's friend described below.

Explain it to a non-expert

The shopper's friend has never studied logic and asks, "The policy says some clearance items can't be returned. So all the other clearance items can be returned, right?" Write a 3–5 sentence message that explains in everyday words what "some" means, reports the percentage you found and how many logged clearance items were not sale items, and names one limit: the policy says which items cannot be returned, not which items can. Explain any technical term in everyday words. More than one good answer is possible.

For a different, ungraded example, imagine a community pool that posts "Some swim lanes are closed for lessons." Model answer: "Some here means at least one lane, nothing more. The sign tells you a lane is closed, but it does not tell you the other lanes are open; they could be closed for cleaning too. Check the lane you want before you plan your swim."

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

Show your arithmetic, describe each Venn diagram region by region, and quote the sentences you use. A reader should be able to reproduce every number you report, and find every quoted sentence in the club rules, 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 what "some" means, reporting the percentage and how many logged clearance items were not sale items, and naming one limit; and
• a one-line restatement of the values you used (the teams and members per team, the members who completed the safety course, and the logged clearance and sale items), 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 labelled sketches of the two three-circle diagrams with each shaded region and each X named and a short note that says the verdict 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, the diagrams, and the writing yourself, without a chatbot or other AI tool. Quote the club rules, 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.

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