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Advanced ⛓ Discrete Math & Number Theory Topic 21 of 103

Inclusion–Exclusion Principle

Count a union by correcting overlaps.

Key idea

Count a union by correcting overlaps.

In depth

|A ∪ B| = |A| + |B| − |A ∩ B|. For three sets: add singles, subtract pairs, add the triple. It corrects for over-counting overlaps and works for any number of sets with alternating signs.

Worked example

Numbers 1–100 divisible by 2 or 3: 50 + 33 − 16 = 67.

Formula

|A∪B| = |A|+|B|−|A∩B|

Real-world uses

Common mistake

Stopping after subtracting pairs and missing the triple intersection.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Inclusion–Exclusion Principle?

Count a union by correcting overlaps. It is a topic at the advanced level in Discrete Math & Number Theory.

What is the formula for Inclusion–Exclusion Principle?

The key formula is |A∪B| = |A|+|B|−|A∩B|.

Where is Inclusion–Exclusion Principle used in real life?

Real-world examples: Counting people who speak English or French without double counting bilinguals.

What should I learn before Inclusion–Exclusion Principle?

Make sure you are comfortable with Venn Diagrams, the previous topic in Discrete Math & Number Theory.

What is a common mistake with Inclusion–Exclusion Principle?

Stopping after subtracting pairs and missing the triple intersection.

How can I practise Inclusion–Exclusion Principle?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Inclusion–Exclusion Principle?

Move on to Cartesian Products next.

Related advanced topics in Discrete Math & Number Theory