Download 2.1 Set Concepts A Set is a collection of objects known as “elements

2.1 Set Concepts
A Set is a collection of objects known as “elements” and is generally named using a capital block-style letter
(A, B, C, etc.).
The symbol
numbers.
Ex.
is used to represent the statement “is an element of.” In mathematics, the elements are often
{
}
NOT { }
{
}
Inclusive: includes boundaries
Example:
 The set of natural numbers between 5 and 8
 The set of natural numbers between 5 and 8, inclusive
A set can be identified using one of the following methods:
Roster:
Set Builder Notation:
Description:
Examples: Each set is described using one method. Describe the same set using the other two methods.
A. Natural numbers from 1 to 5 inclusive
B. { x x  W}
C.
{…,-2, -1, 0, 1, 2,…}
Ex. Write B = { 1, 2, 3, 4, 5 } in set – builder notation.
Ex. Write the following in roster form:
The set of football players over the age of 70 who are still playing in the NFL
Ex. Write a description of the following set:
D = {1,2,3,4,5,6}
Set Vocabulary
Finite Set:
Ex:
Infinite Set:
Ex:
Well Defined:
Ex:
Cardinality:
Ex:
Empty Set or Null Set:
Ex:
Universal Set:
Ex:
Equivalent:
Ex:
Equal:
Ex:
 If two sets are equal, they are also equivalent.
 If two sets are equivalent, they are not necessarily equal.
Practice Problems
Determine whether the set is well defined or not well defined.
1) The set of the best luggage
1) _____________________
2) The set of children in first grade at Maple Elementary School that are boys
2) _____________________
Identify the set as finite or infinite.
3) {10, 11, 12, . . ., 40}
3) _____________________
4) {
4) _____________________
}
5) The set of multiples of 2 between 0 and 50
5) _____________________
Express the set in roster form.
6) {x | x is a whole number between 1 and 5}
6) _____________________
7) {x | x is an integer greater than -6}
7) _____________________
8) {x | x is a natural number less than -2}
8) _____________________
9) The set of the days of the week
9) _____________________
Write the set in set-builder notation.
10) {15, 16, 17, 18}
10) ___________________
11) {24, 30, 36, 42,..., 84}
11) ___________________
Tell whether the statement is true or false. If false, give the reason.
12) 5
{10, 15, 20, 25, 30}
12) ___________________
13) {4, 10, 12} = {0, 4, 10, 12}
13) ___________________
14) 17 ∉ {16, 14, 13, . . ., 1}
14) ___________________
Find n(A) for the set.
15) A = {6, 8, 10, 12, 14}
15) ___________________
16) A = {x | x is a number on a clock face}
16) ___________________
17) A = {x∣x
17) ___________________
N and 15 ≤ x ≤ 23}
Solve the problem.
18) Use the following table, which shows the average price for a new beverage that is served at a coffee chain. Let
the 10 selected regions represent the universal set. Use the list to represent the set in roster form.
The set of regions in which the average price for the new beverage is more than $5.00.
18) ___________________
19) Use the following graph, which shows the sales of digital music players, in millions, at a national
electronics retail store for the years 2005-2012. Use the graph to represent the set in roster form.
2005 2006 2007 2008 2009 2010 2011 2012
Year
The set of years included in the graph in which digital music player sales were between 2 and 5 million.
19) ___________________
Determine whether the sets are equal, equivalent, both, or neither.
20) {63, 18, 100} and {18, 100, 63}
20) ___________________
21) {4, 13} and {41, 3}
21) ___________________
22) {2, 15} and {2, 1, 5}
22) ___________________
23) {1/10, 2/10, 3/10} and {0.1, 0.2, 0.3}
23) ___________________
Write a description of the set.
24)
{
25)
{ |
}
24)____________________________________________________________
≤ }
25)____________________________________________________________