Exercises. Section 2.1 The Language of Sets
Use set notation to list all of the elements of this set:
{y : y is an even natural number less than 6}
{2,4}
‘Natural number’ is another name the for
‘counting number’ { 1, 2, 3, … }
Use set notation to list all of the elements of this set:
{-21, -17, -13, … , 7}
{-21, -17, -13, -9, -5, -1, 3, 7}
4
4
First notice that these
numbers are 4 units apart.
4 4 4 4 4
Use set-builder notation to express this set:
{6, 12, 18, 24, …}
{x : x is a natural number and a multiple of 6 }
Is this set well defined?
{t : t has a nice house}
Most would
probably agree
that the meaning
of ‘nice’ varies a
lot from person
to person so it
would be hard to
think of the set
TYPES
beingOF
well
defined.
DO NOT OVERTHINK THESE
QUESTIONS!!
No
one
is
trying
to
trick
you
here.
A set is well defined if it is possible to
determine if a given object is included in
the set.
Without overthinking this,
NO, this set is not well defined.
Is this set well defined?
{x : x lives in Texas}
The Texas border is
fixed, and although,
if you think hard
enough, you might
be able to imagine a
situation where it
wouldn’t be clear
that a person did or
did not live in Texas,
we aren’t supposed
to have to do that.
DO NOT OVERTHINK THESE TYPES OF
QUESTIONS!!
No one is trying to trick you here.
A set is well defined if it is possible to
determine if a given object is included in the
set.
Without overthinking this,
YES, this set is well defined.
16 # {x : x is a rational number}
Replace ‘#’ with ‘∈’ or ‘∉ ’ to make the
statement true:
16 ∈ {x : xAis‘rational
a rational
number}
number’ is one that can be written as
a RATIO
of two integers.
And remember, the set of integers is the set of
counting numbers (the positive integers) plus
the set of negative integers plus zero.
{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }
16 can be written as the ratio of two integers in many ways:
For example, as
16
1
or
32
2
… so, 16 is a rational number.
So, 16 ∈ {x : x is a rational number}
Find n(A) for the following set A.
A = {103, 104, 105, 106, … , 123}
The number of elements in set A is called the cardinal number of set A.
The cardinal number of a set A is denoted n(A).
So, we just need to count the elements in A.
Shortcut for counting CONSECUTIVE
integers:
LARGEST – SMALLEST + 1
So, n(A) = 123 – 103 + 1
n(A) = 21
Find n(A) for the following set A.
A = {x : x is a woman who served as U.S. Vice
President before 1900}
I hope that you know without
having to ask YAHOO! answers
like this person did:
n(A) = 0
Describe the following set as either finite or infinite.
{All multiples of 4 that are greater than 19}
The number of elements in set A is called the cardinal number of set A.
The cardinal number of a set A is denoted n(A).
A set is finite if its cardinal number is a whole number.
An infinite set is one that is not finite.
The set of whole numbers are the
counting numbers PLUS zero.
{ 0 , 1 , 2 , 3, 4
,…}
{y : y is a number between 7 and 14}
101
10
8.1
12.999907
13.4
Number is a very generic
term so this could be
ANY number
8
8.0001
… 𝑎𝑛𝑑 𝑤𝑒 𝑐𝑎𝑛 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑒 𝑓𝑖𝑛𝑑𝑖𝑛𝑔
𝑛𝑒𝑤 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑖𝑛 𝑡ℎ𝑖𝑠 𝑟𝑎𝑛𝑔𝑒 𝑓𝑜𝑟𝑒𝑣𝑒𝑟.
{y : y is an integer between 7 and 14}
= { 8 , 9 , 10 , 11 , 12 , 13 }
Use table info below to describe this set in an
alternative way:
{Class A, Class B, Class D, Class E, Class F}
{ x : x is a Humanities class }