MathematicsChapter 3: Sets and Relations
The Inclusion Formula
If n(S) means 'number of elements,' then n(A union B) = n(A) + n(B) - n(A intersect B).
Learning objectives
- Define and explain the inclusion formula.
- Apply the inclusion formula to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
If n(S) means 'number of elements,' then n(A union B) = n(A) + n(B) - n(A intersect B). You add both sizes, then subtract the overlap once so it is not double-counted. If A and B are disjoint, the intersection is empty, n(A intersect B) = 0, and the formula becomes n(A) + n(B).
Where / symbols
- The Inclusion Formula
- If n(S) means 'number of elements,' then n(A union B) = n(A) + n(B) - n(A intersect B). You add both sizes, then subtract the overlap once so it is not double-counted. If A and B are disjoint, the intersection is empty, n(A intersect B) = 0, and the formula becomes n(A) + n(B).
Relationship
- n(A union B) = n(A) + n(B) - n(A intersect B)
Overview
Learn the idea, then use it:
Core Understanding
If n(S) means 'number of elements,' then n(A union B) = n(A) + n(B) - n(A intersect B). You add both sizes, then subtract the overlap once so it is not double-counted. If A and B are disjoint, the intersection is empty, n(A intersect B) = 0, and the formula becomes n(A) + n(B).
Examples n(A union B) = n(A) + n(B) - n(A intersect B) · associative · distributive · THE INCLUSION FORMULA: If n(S) means 'number of elements,' then n(A union B) = n(A) + n(B) - n(A intersect B). You add both sizes, then subtrac
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — THE INCLUSION FORMULA
If n(S) means 'number of elements,' then n(A union B) = n(A) + n(B) - n(A intersect B). You add both sizes, then subtract the overlap once so it is not double-counted. If A and B are disjoint, the intersection is empty, n(A intersect B) = 0, and the formula becomes n(A) + n(B).
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge the inclusion formula with a neighbouring idea that uses a different definition, rule, or method.
Key points
- n(A union B) = n(A) + n(B) - n(A intersect B)
- associative
- distributive
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.The Inclusion Formula
Sticky Notes · Quick Revision
Core Idea
- If n(S) means 'number of elements,' then n(A union B) = n(A) + n(B) - n(A intersect B).
Key Points
- n(A union B) = n(A) + n(B) - n(A intersect B)
- associative
- distributive
Simple Check
- Explain the inclusion formula in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge the inclusion formula with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- If n(S) means 'number of elements,' then n(A union B) = n(A) + n(B) - n(A intersect B).
- n(A union B) = n(A) + n(B) - n(A intersect B)
- associative
- distributive
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