Kenneth ChengMathematical modeling
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Find the cardinality of the complement.

Read the idea, work independently, then explain what changed.

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TOPIC 01

Sets and commonly used logic: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

Find the cardinality of the complement.

A⊆U, ∣U∣=26, ∣A∣=9A\subseteq U,\ |U|=26,\ |A|=9
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Translate membership into “and”, “or”, or “not”.
Hint 2
Partition the universal set into two disjoint parts.
Worked solution

  1. Translate membership into “and”, “or”, or “not”.

  2. Calculate or simplify this relation.

    ∣U∖A∣=26−9=17|U\setminus A|=26-9=17

  3. The complement depends on the specified universal set.

The requested value is 17.

Checks and common pitfalls: The complement depends on the specified universal set.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗