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