Definition
Union of sets
The union of sets contains every element that belongs to at least one of those sets.
Continue from this idea into connected AXIO math.
Pour the sets into one bowl, then keep one of each element.
Boundary: Keeping only the elements shared by both sets gives the intersection, not the union.
What it means
To make a union, gather everything from the sets into one new set. Keep every element that appears in either set or in both sets, but write each element only once. The union symbol is ∪.
Remember it
Pour the sets into one bowl, then keep one of each element.
Example
Let A = {1, 3, 5} and B = {3, 4}. Then A ∪ B = {1, 3, 4, 5}. The element 3 is in both sets, but it is listed once in the union.
Watch for
Keeping only the elements shared by both sets gives the intersection, not the union.
Common mix-up
In a union, “or” includes elements that are in both sets as well as elements in only one.
Exact meaning
The union of two or more sets is the set of all elements that belong to at least one of them. It uses inclusive “or”, and an element in an overlap appears only once in the union.