Week 5 — Who Is In, Who Is Out: Testing Rules About Groups

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 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 4 you learned to read an "if" sentence exactly as it is written; this week you read sentences about groups the same careful way and test the syllogisms people build from 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 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.

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, describe each Venn diagram region by region, 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 member's syllogism valid because both premises are about hike leaders, or reads "some" as "some but not all", 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 everyday sentences into the four categorical forms, naming the terms of a categorical syllogism, testing a syllogism with a three-circle Venn diagram described in words, and reading "some" as "at least one". 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, club, or store, and never use logic symbols. Do not name any informal fallacy, and do not use mood, figure, or distribution-rule names.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The texts: an illustrative set of hiking-club rules, "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." And an illustrative store policy, "No sale items are returnable items. Some clearance items are sale items." 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."
PROBLEM P1: The club rules say the club has 4 teams of 15 members each. How many members does the club have in all?
PROBLEM P2: Using the member total from Problem 1, how many members have not completed the safety course?
PROBLEM P3: The store log says 12 of the last 40 clearance items sold were sale items. What percentage of those clearance items were sale items?
PROBLEM P4: Of the same 40 logged clearance items, how many were not sale items?
After the four answers, I must briefly interpret each one: for P1, rewrite the club's first rule into a categorical form, name its subject and predicate terms, and say one thing it does not say; for P2, test the member's syllogism with a Venn diagram described in words, give the verdict, and describe a counterexample built from a member who has not completed the safety course; for P3, test the shopper's syllogism with a Venn diagram described in words, give the verdict, and name its middle term; for P4, explain whether the policy says anything about whether the clearance items that were not sale items can be returned. I must then write a 3-5 sentence message to the shopper's friend explaining what "some" means, reporting the percentage and the number of clearance items that were not sale items, 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 member 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 every part named for that problem = 2; at least one part but not all = 1; none = 0. For P4, BOTH an explanation of whether the policy says anything about the clearance items that were not sale items AND a friend message that explains what "some" means, 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 the member's syllogism 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 club rules, 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. When I describe a Venn diagram, ask me which region I shaded or marked and why, region by region. 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 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;
• 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 5 skills — rewriting everyday sentences into the four categorical forms, naming the terms of a syllogism, testing a syllogism with a Venn diagram described in words, reading "some" as "at least one", and explaining what a rule does not say 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 club rules, 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 club rules, 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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