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Grade 9 · lesson 3 of 4

Diagnose the stated logic condition

Trace the rule and facts exactly. Choose the demonstrated condition, keeping truth of premises separate from validity of the inference.

About 22 minutes, plus any extended practice

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Supplied materials

  • Paper and pencil, or a browser text area. All named people/events/records are fictional learning inputs.
  • Worked case: Excerpt A: Who benefits from a label nobody can read? The writer asks this to prompt thought rather than solicit a factual count. Excerpt B: All required parts in this kit need labels. This part is required. Therefore it needs a label. Analyze the first sentence. Excerpt C: Rule: Every registered model needs a label. A is registered. Therefore A needs a label. Excerpt D: Procedure for staff: place each label beside its matching part and record the location.
  • Primary check: Excerpt A: We need clear names, clear diagrams and clear limits. The three phrases share the same grammatical shape. Excerpt B: All required parts need labels. The hinge is required. Therefore it needs a label. Analyze the second sentence. Excerpt C: If a model is ready, it has labels. This model has labels, so it must be ready; other models may have labels before testing. Excerpt D: For new builders: a hinge, a joint that permits movement, connects the two panels.

Learn the idea

Reasoning forms matter. If A then B and A allows B; B alone does not prove A. A narrow sample cannot establish everyone, and correlation alone does not demonstrate cause.

Trace the rule and facts exactly. Choose the demonstrated condition, keeping truth of premises separate from validity of the inference.

Original worked input: Original excerpt C: Rule: Every registered model needs a label. A is registered. Therefore A needs a label. The task is to diagnose the stated logic condition. The answer is “valid application of a stated rule”. Evidence: Rule: Every registered model needs a label. A is registered. Therefore A needs a label. Reasoning: valid application of a stated rule is supported because given the stated rule and membership fact, the conclusion follows, including the contrapositive of a necessary condition. A valid structure can still start from a false premise.

  1. Read the supplied worked case and identify the part named in this lesson. An adult can model unfamiliar words.
  2. Trace the rule and facts exactly. Choose the demonstrated condition, keeping truth of premises separate from validity of the inference.
  3. Check the worked solution: valid application of a stated rule. Evidence: Rule: Every registered model needs a label. A is registered. Therefore A needs a label. Reasoning: valid application of a stated rule is supported because given the stated rule and membership fact, the conclusion follows, including the contrapositive of a necessary condition. A valid structure can still start from a false premise.
  4. Use the new primary and practice cases. Give a reason from the actual words before checking the feedback.
Worked example

See the method in action

Original excerpt C: Rule: Every registered model needs a label. A is registered. Therefore A needs a label. Solved: valid application of a stated rule. Evidence: Rule: Every registered model needs a label. A is registered. Therefore A needs a label. Reasoning: valid application of a stated rule is supported because given the stated rule and membership fact, the conclusion follows, including the contrapositive of a necessary condition. A valid structure can still start from a false premise. Trace the rule and facts exactly. Choose the demonstrated condition, keeping truth of premises separate from validity of the inference.

Your turn

Check your reasoning

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Helpful tips
  • If rain then wet does not mean wet implies rain.
  • A valid structure can still start from a false premise.
Original excerpt C: If a model is ready, it has labels. This model has labels, so it must be ready; other models may have labels before testing. Use excerpt C only. Which logic condition is explicitly demonstrated?

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

affirming the consequent

Evidence: If a model is ready, it has labels. This model has labels, so it must be ready; other models may have labels before testing. Reasoning: affirming the consequent is supported because having the rule’s consequent is treated as proof of its antecedent, though another cause is allowed. A valid structure can still start from a false premise.

Take it further

Changed-input task: Original excerpt C: Two people liked the display, so the writer claims all residents liked it. Give an evidence-based answer before looking at the model. Expected reasoning: Evidence: Two people liked the display, so the writer claims all residents liked it. Reasoning: overgeneralization is supported because a few cases are asserted to establish every case. A valid structure can still start from a false premise. Then write a brief alternative sentence, paragraph, source note or scene that demonstrates the same operation; label new fictional details and preserve source limits.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.

More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. Original excerpt C: The lamp was added when attendance rose. No comparison excludes weather or publicity, but the writer says the lamp caused the rise. Use excerpt C only. Which logic condition is explicitly demonstrated?
Need a hint?
  • If rain then wet does not mean wet implies rain.
  • A valid structure can still start from a false premise.
2. Original excerpt C: Two volunteer results are said to prove every learner’s result, with no representative evidence. Use excerpt C only. Which logic condition is explicitly demonstrated?
Need a hint?
  • If rain then wet does not mean wet implies rain.
  • A valid structure can still start from a false premise.
3. Original excerpt C: All eligible records have dates. A lacks a date, so it is not eligible under that stated rule. Use excerpt C only. Which logic condition is explicitly demonstrated?
Need a hint?
  • If rain then wet does not mean wet implies rain.
  • A valid structure can still start from a false premise.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.