LEARN · EXPLAIN · REVISE

Prove the complement-of-union rule.

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

U\setminus(A\cup B)

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

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

Hint 2

Negate “in A or in B”.

Worked solution

Translate membership into “and”, “or”, or “not”.
Calculate or simplify this relation.
$x\notin A\cup B\iff(x\notin A)\land(x\notin B)$
Negating “or” produces “and”.

It equals (U∖A)∩(U∖B).

Checks and common pitfalls: Negating “or” produces “and”.

Reasoning checklist · self / teacher assessment

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.