Kenneth ChengMathematical modeling
← Senior Mathematics Studio

LEARN · EXPLAIN · REVISE

How many proper subsets does A have?

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

Return to the lesson / paper ↗

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

How many proper subsets does A have?

∣A∣=8|A|=8
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Apply the element-by-element definition of inclusion.
Hint 2
Remove only the full set.
Worked solution

  1. Apply the element-by-element definition of inclusion.

  2. Calculate or simplify this relation.

    28−1=2552^{8}-1=255

  3. For a nonempty set, the empty set remains a proper subset.

The requested value is 255.

Checks and common pitfalls: For a nonempty set, the empty set remains a proper subset.

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 ↗