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Find the interval intersection.

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

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

Revisit first: Basic relations between sets

TOPIC 01

Basic operations on sets

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

What you will be able to explain

Apply basic operations on sets with explicit conditions.
Connect representations and justify the steps, including boundary cases.
Explain a solution and apply the idea to a changed situation.

Try it. Leave your reasoning visible.

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

01 / Standard#Your turn

Find the interval intersection.

[-3,6)\cap(3,10]

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

Use the tighter bound at each end.

Worked solution

Translate membership into “and”, “or”, or “not”.
Calculate or simplify this relation.
$3<x<6$
Each endpoint fails at least one original condition.

The intersection is (3,6).

Checks and common pitfalls: Each endpoint fails at least one original condition.

Reasoning checklist · self / teacher assessment

State the relevant definition, condition or model.
Show a valid calculation, proof or counterexample.
Interpret the conclusion with its restrictions.

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

Teacher preparation and assessment

Question sequence

What must be true before using the main rule for basic operations on sets?
Which representation makes this task easier, and why?
Change one assumption. Does the conclusion survive?

Board plan

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.

Anticipated thinking

Expected reasoning: Intersection uses both conditions; union uses at least one.
Expected reasoning: A complement is relative to a specified universal set.
Expected correction: Do not count the overlap twice.

Assessment checklist

1: identify the givens and required quantity.
1: choose a valid definition, representation or method.
1: present connected, correct reasoning.
1: check conditions and explain the result.