A set is the mathematical name given to a group of items that share some common property. All positive numbers make up one set, and all prime numbers make up another. Each item in a set is called an element or a member.

Don’t confuse a set with a sequence. A set is simply a collection of elements that are not necessarily related to one another, as they are in a sequence.

The union of two sets is another set that contains all the elements of each set. If set A contains all the blue-eyed women and set B contains all the blue-eyed men, the union of sets A and B is all blue-eyed women and men. If set A = (1, 2, 4, 6, 8) and set B = (2, 3, 5, 7, 8), the union of A and B is (1, 2, 2, 3, 4, 5, 6, 7, 8, 8).

The intersection of two sets is another set that contains all the elements the two sets have in common. If set A = (1, 2, 4, 6, 8) and set B = (2, 3, 5, 7, 8), the intersection of A and B is the set (2, 8).

A difficult set item involves a group of people, some of whom are engaged in activity A and others in activity B, while still others refrain from participating in either activity. Here’s an example:

To solve this item, use the following simple formula:

You have to figure out which members belong to set 1, which to set 2, what the intersection of two sets is, and how many abstain from participating.

There are a total of 26 students, choice C.

Some set items may not explicitly tell you how many people are in neither set. If an item says that each student in a class has to learn either French or Italian, then the “neither set” (those learning neither French nor Italian) is zero.

That covers the numbers & operations basics. Now let’s apply these concepts to some SAT strategies.