Sets

Section 1What a set is

A set is a well-defined collection of objects, numbers, or people. The objects in a set are called elements. For example, the set of vowels in the word JAMAICA is {A, I}; repeated letters are not listed twice in a set.

Section 2Set notation

Sets are often named with capital letters like A, B, and C. Elements are placed inside braces, such as A = {2, 4, 6, 8}. If 4 is in A, we say 4 is an element of A. If 5 is not in A, we say 5 is not an element of A.

Section 3Universal set and empty set

The universal set contains every element being considered in a question. It is usually written as U. The empty set has no elements and may be written as { } or with the empty-set symbol. Watch out: {0} is not empty because it contains the element 0.

Section 4Subsets and complements

A subset is a set whose elements are all found inside another set. If A = {2, 4} and B = {2, 4, 6}, then A is a subset of B. The complement of A means all elements in the universal set that are not in A.

Section 5Union and intersection

The union of A and B means elements in A or B or both. The intersection of A and B means elements that are in both A and B. Easy to mix up - union gathers everything from the sets, while intersection keeps only the overlap.

Section 6Venn diagrams

A Venn diagram uses circles inside a rectangle to show sets inside the universal set. The overlap represents the intersection. The region outside the circles but inside the rectangle represents elements in the universal set that are not in those sets.

Section 7Counting with Venn diagrams

When two sets overlap, place the intersection first so you do not count it twice. Then fill the only-A and only-B regions. Here's the trick: total in A union B = only A + overlap + only B.