Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Or search for something specific

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

Mathematics

The Principle of Inclusion-Exclusion for Counting Union of Sets

Quick fact

For three sets A, B, and C, the number of elements in their union is |A|+|B|+|C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|. This alternating pattern—add all, subtract pairwise, add triple—applies for any number of sets.

Why this is interesting

You have a bag of red marbles, a bag of blue marbles, and some that are both. How many distinct marbles are there in total? Simply adding the counts would count the mixed ones twice—so what's the right way?

Private administrator preview

Subjects · study & training · careers

What would you like to explore?

Choose something you are considering. FACTREE will give you a clear picture of what it contains, how its main parts connect and where it could lead.

This private catalogue connects 31 subjects, study routes and careers across six broad areas. Public Maps and learner routes remain off.

Curiosity quiz

What do you already know?

One question at a time. A wrong answer is simply another way into something worth knowing.

Science & medicine

Question 1

Finding a question for you…

Administrator

Manage FACTREE.

Review learner demand, card visibility and private knowledge-architecture evidence.

Profile

Sign-in & security

Sharing

Your data

Your next discovery is one click away.

The Principle of Inclusion-Exclusion for Counting Union of Sets

Let a fact find you.

Stop FACTREE emails?

You’re unsubscribed

What would you like to explore?

Choose a subject

Programming

Programming

What do you already know?

Finding a question for you…

Manage FACTREE.

Choose a path

Discovery coverage workbench

Choose a subject

Continue exploring