MathematicsChapter 3: Sets and Relations
Counting
With three sets A, B, C inside a universal set, a Venn diagram has seven inner regions plus the outside.
Learning objectives
- Define and explain counting.
- Apply counting to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
With three sets A, B, C inside a universal set, a Venn diagram has seven inner regions plus the outside. Start filling from the triple overlap A n B n C, then the pairwise-only regions, then only-A, then outside. Inclusion-exclusion: n(A u B u C) = n(A)+n(B)+n(C) - n(A n B)-n(B n C)-n(C n A) + n(A n B n C).
Where / symbols
- Counting
- With three sets A, B, C inside a universal set, a Venn diagram has seven inner regions plus the outside. Start filling from the triple overlap A n B n C, then the pairwise-only regions, then only-A, then outside. Inclusion-exclusion: n(A u B u C) = n(A)+n(B)+n(C) - n(A n B)-n(B n C)-n(C n A) + n(A n B n C).
Overview
Learn the idea, then use it:
Core Understanding
With three sets A, B, C inside a universal set, a Venn diagram has seven inner regions plus the outside. Start filling from the triple overlap A n B n C, then the pairwise-only regions, then only-A, then outside. Inclusion-exclusion: n(A u B u C) = n(A)+n(B)+n(C) - n(A n B)-n(B n C)-n(C n A) + n(A n B n C).
Examples fill from the centre · inclusion-exclusion
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 — COUNTING
With three sets A, B, C inside a universal set, a Venn diagram has seven inner regions plus the outside. Start filling from the triple overlap A n B n C, then the pairwise-only regions, then only-A, then outside. Inclusion-exclusion: n(A u B u C) = n(A)+n(B)+n(C) - n(A n B)-n(B n C)-n(C n A) + n(A n B n C).
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 counting with a neighbouring idea that uses a different definition, rule, or method.
Key points
- fill from the centre
- inclusion-exclusion
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Counting
Sticky Notes · Quick Revision
Core Idea
- With three sets A, B, C inside a universal set, a Venn diagram has seven inner regions plus the outside.
Key Points
- fill from the centre
- inclusion-exclusion
Simple Check
- Explain counting 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 counting 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
- With three sets A, B, C inside a universal set, a Venn diagram has seven inner regions plus the outside.
- fill from the centre
- inclusion-exclusion
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