# Set operations

A set is a collection of distinct objects. The union joins two sets, the intersection keeps what they share, and A minus B removes B's members from A.

Maths (university) · Part 01: Logic, sets and proof · Card 8 of 9 · Last updated 2026-10-19

## Analogy

Two friends' music libraries: the union is everything either owns, the intersection is songs both own.

## Example

**A = {1,2,3,4}, B = {3,4,5}**

Union: {1,2,3,4,5}
Intersection: {3,4}
A minus B: {1,2}
B minus A: {5}

## In practice

Domains of functions, solution sets and events in probability are all sets, so these operations appear everywhere.

## Practice

### Flashcards

- **What is A intersect B for A = {1,2,3,4} and B = {3,4,5}?** {3, 4}.

## Questions people ask

### What is the difference between a union and an intersection?

A union contains everything that is in at least one of the sets. An intersection contains only elements that are in both. For A = {1,2} and B = {2,3}, the union is {1,2,3} and the intersection is {2}. Remember union as 'or' and intersection as 'and'.

### What is the empty set and why does it matter?

The empty set has no elements and is written with a slashed circle or empty braces. It is the answer when two sets share nothing, such as even numbers and odd numbers. It is a subset of every set, which keeps many proofs tidy.

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