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set builder notation 2={12, 13,14,15,16,17,28,19,20}

by Diana
(Indianapolis)










































using correct mathematical notation and symbols, express the following in set builder notation 2={12, 13,14,15,16,17,28,19,20}

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Mar 11, 2012
Set Builder Notation
by: Staff


Question:

by Diana
(Indianapolis)

using correct mathematical notation and symbols, express the following in set builder notation 2={12, 13,14,15,16,17,28,19,20}


Answer:

Set 2 = {12, 13,14,15,16,17,28,19,20}

Four different ways of representing set Z are shown below:

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




1. ROSTER Notation:

Set 2 = {12, 13,14,15,16,17,28,19,20}



2. SET BUILDER Notation:

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


Here is a commonly used format:


Set 2 = {n | n ∈ ℕ, 12 ≤ n ≤ 20}


{} 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 ∈ N,
ℕ (the set of all natural numbers) is the“input set”
12 ≤ n ≤ 20 is the “predicate”


Reading from left to right: “Z” is the set of all numbers “n” {n | … , …} where “n” is an element of the set of natural numbers ℕ { … | n ∈ ℕ, … } and “n” is greater than or equal to 12 and less than or equal to 20 {… | … , 12 ≤ n ≤ 20}.




3. INTERVAL Notation:

This is a “closed interval”. The endpoints of 12 and 20 “are included” in the interval. Therefore [ ] must be used to show the interval.

However, this notation CANNOT BE USED: Set 2 = [12, 20]. [12, 20] means all REAL numbers between from 12 through 20 (including endpoints)

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

Interval Notation for Integers should be written:

Set 2 = [12 . . 20]


It should be read: the set of all integers beginning with (and including) 12 and ending with (and including) 20.






4. GRAPHICAL Representation:

Set 2 = {12, 13,14,15,16,17,28,19,20}


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

(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/graph-set-2012-03-11.png



Thanks for writing.

Staff
www.solving-math-problems.com

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