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:
a group of students, 24 are considered to be good at math, 14 are good
at liberal arts, and 12 are good at both. How many students are
in the group?
To solve this item, use the following simple formula:
Total in a set = number in set 1 + number in set
intersection of set 1 and set 2 + number in neither set
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.
Total students = those in math (24) + those in
liberal arts (14) –
those in both (12) + those in neither (0) = 26.
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.