Algebra - Sets
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Algebra - Sets

by Marcus
(Benjamin)










































1.
Choose the correct solution in roster form and in set-builder notation.

N is the set of real numbers that are factors of 12
(1 point)

Comments for Algebra - Sets

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Jan 06, 2012
Algebra – Set Notation
by: Staff


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Part II


3. INTERVAL Notation:

This is a “closed interval”. The endpoints of -12 and 12 “are included” in the interval. Therefore [ ] must be used to show the interval.

However, this notation CANNOT BE USED: N = [-12, 12]. [-12, 12] means all REAL numbers between from -12 through 12 (including endpoints)

Your set includes only INTEGERS. Your set does not include any other real numbers.

Interval Notation for Integers should be written in this format: [-12 . . 12]


For your specific set of N = {-12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12}

One way to write the same set in interval notation is:

N = [-12] ∪ [-6] ∪ [-4 . . -1] ∪ [1 . . 4] ∪ [6] ∪ [12]

It should be read: the set of all integers beginning with (and including) -12 in union with -6 in union with the set of integers -4 through -1 (including the -4 and the -1) in union with the set of integers 1 through 4 (including the 1 and the 4) in union with the integer 6 in union with (and including) the integer 12


4. GRAPHICAL Representation:

N = {-12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12}

Open the link shown below to view the graphical representation of set N:

(1) If your browser is Firefox, click the following link to VIEW ; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/Graphical-Representation-set-N-2012-01-06.png



Thanks for writing.
Staff
www.solving-math-problems.com


Jan 06, 2012
Algebra – Set Notation
by: Staff


Part I

Question:

by Marcus
(Benjamin)


1. Choose the correct solution in roster form and in set-builder notation.

N is the set of real numbers that are factors of 12
(1 point)





Answer:

Set N = the set of real numbers that are factors of 12

Factors of 12: 1*12, 2*6, 4*3
Factors of 12: (-1)*(-12), (-2)*(-6), (-4)*(-3)

The Prime Factors of 12 = 2*2*3, all prime factors are positive numbers

All the factors of 12: 1, 2, 3, 4, 6, 12 and -1, -2, -3, -4, -6, -12


Four different ways of representing set N are shown below:

1. ROSTER Notation
2. SET BUILDER Notation
3. INTERVAL Notation
4. GRAPHICAL Representation




1. ROSTER Notation:

N = {-12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12}



2. SET BUILDER Notation:

There is more than one format for writing this sequence in Set Builder Notation.

Here is a commonly used format:

N = {n | n ∈ ℤ, (-12 ≤ n ≤ 12) and (12/n∈ ℤ)}


{} curly brackets surround the expression

∈ = element of a set

| and : can be used interchangeably. Both notations are separators which mean “where” or “such that”

n: the first “n” is the “output function”, shown as = {n |

n: the second “n” is the “variable”, shown as | n ∈ ℤ,

ℤ (the set of all integers) is the“input set”

(-12 ≤ n ≤ 12) and (12/n∈ ℤ) is the “predicate”


Reading from left to right: N = {n | n ∈ ℤ, (-12 ≤ n ≤ 12) and (12/n∈ ℤ)}

“N” is the set of all numbers “n” {n | … , …}

. . . where “n” is an element of the set of integers ℤ { … | n ∈ ℤ, … }

. . . and “n” is greater than or equal to -12 and less than or equal to 12 {… | … , (-12 ≤ n ≤ 12) and …}

. . . and “n/12” is also an element of the set of integers ℤ {… | … , … and (12/n∈ ℤ)}.

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