LEARN · EXPLAIN · REVISE

Find the cardinality of the complement.

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

高一必修第一册(A版).pdf · 1.3 · PDF 17 / printed page 10

TOPIC 01

Basic operations on sets

Build understanding of basic operations on sets through definitions, contrasting cases and justified applications.

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

01 / Foundation#Your turn

A\subseteq U,\ |U|=14,\ |A|=5

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

The requested value is 9.

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

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

Teacher preparation and assessment

Apply basic operations on sets with explicit conditions.
And / or: Intersection uses both conditions; union uses at least one.
$A\cap B,\quad A\cup B$
Complement: A complement is relative to a specified universal set.
$U\setminus A$
Close with: conditions → representation → reasoning → check.