Definition
Intersection of sets
The intersection of sets contains the elements shared by every set being compared.
Continue from this idea into connected AXIO math.
Intersection means shared by all: keep only the overlap.
Boundary: When no element belongs to every set, the intersection is the empty set, written ∅.
What it means
Imagine checking several club lists and keeping only the names that appear on every list. That kept group is the intersection. In a Venn diagram, it is the overlap that satisfies all the set rules at once.
Remember it
Intersection means shared by all: keep only the overlap.
Example
Let A be the even numbers less than 10: {2, 4, 6, 8}. Let B be the whole numbers greater than 5 and less than 10: {6, 7, 8, 9}. The shared elements are 6 and 8, so A ∩ B = {6, 8}.
Watch for
When no element belongs to every set, the intersection is the empty set, written ∅.
Common mix-up
Intersection means “and” and keeps common elements. Union means “or” and gathers elements from either set.
Exact meaning
The intersection of two or more sets is the set of elements that belong to every one of them. For two sets A and B, it is written A ∩ B and means “in A and in B.”