LEARN · EXPLAIN · REVISE

Among t+8 students, t study art, 8 study music and 3 study both. How many study either subject?

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

TOPIC 01

Counting principles: mixed review

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

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

01 / Standard#Your turn

t=29

Addition requires disjoint cases; stage counts must hold for each branch or use separate branches.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Decide whether choices are alternative cases or successive stages, then check overlap.

Hint 2

Use this intermediate relation.

|A\cup B|=|A|+|B|-|A\cap B|

Worked solution

Decide whether choices are alternative cases or successive stages, then check overlap.
Apply the stated relation and retain its conditions.
$N=29+8-3=34$
Subtract the overlap once because it was counted twice.

The requested value is 34.

Checks and common pitfalls: Subtract the overlap once because it was counted twice.

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

Teacher preparation and assessment