Sets
Set is a fancy math word for a group
of items. Each item in a set is called an
element or
a
member. The entire number of Hummers Jay-Z owns
is a set, and each of the Hummers is an element of the set. A set
contains only those things that can fit its definitions. Jay-Z’s
Ferraris and BMWs can’t be in the set of his Hummers. If you have
a set that is defined as
(1, 2,
), then the only things that can
be in that set are
(1, 2,
).
Union and Intersection
The union of two sets is a set containing each element
found in either set. If set A contains all the birds in the world,
and set B contains all the fish in the world, then the union of
those sets contains all the birds and all the fish in the world.
If set A = (1, 6, 7, 8, 11, 13) and set B =(2, 4, 5, 8), then the
union of set A and B is (1, 2, 4, 5, 6, 7, 8, 8, 11, 13).
The intersection of two sets are the elements common to
each set. The intersection of the set that contains all the fish
in the world with the set that contains all the birds in the world
is an empty set ( ), because there are no animals that are both
fish and birds. The intersection of set A = (1, 6, 7, 8, 11, 13)
and set B = (2, 4, 5, 8) is (8), since both set A and set B contain
an 8.
The Difficult Set Question
One particular type of set question almost always comes
up on the SAT, and just as often throws students for a loop. In
this type of question, the SAT describes two sets and a few people
or things that fit into both sets. Then it asks how many total are
in the two sets.
|
|
|
Of
the lions at the zoo, 13 eat zebra meat, 11 eat giraffe meat, and
7 eat both. How many lions are there in the zoo? |
|
This question just feels hard. Lots of
students who haven’t read this book will skip it. But you have read
this book, and you’ll know the (surprisingly simple) formula for getting
it right:
Total = number in set 1 + number in set 2
– number common to set 1 and 2
Once you know the formula, all you have to do is figure
out which numbers in the word problem define set 1,
which define set 2, and which define the overlap set. After
that, just plug in the numbers and do some simple addition and subtraction.
So how many lions are there in the zoo?
Total lions = 13 zebra eaters + 11 giraffe
eaters – 7 eaters of both
Total Lions = 13 + 11 – 7 = 17
That’s it for Numbers and Operations. Ready for SAT algebra?
You bet you are.
