logo for solving-math-problems.com
leftimage for solving-math-problems.com

Sub Sets

by J galyon
(California)










































List all the subsets of { 8, 15, 28, 41, 60}

Every subset contains at least one of the elements the set.

For example, { 8} and { 15, 60} are both subsets of { 8, 15, 28, 41, 60}.

Comments for Sub Sets

Click here to add your own comments

Jan 17, 2012
All Possible Subsets of a Set
by: Staff


---------------------------------------

Part II



Selecting any 1 element from the 5 possible choices = 5 subsets possible

C(5,1) = 5! / 1! (5 - 1)!

C(5,1) = (5*4*3*2*1) / 1*4*3*2*1

C(5,1) = 5 / 1

C(5,1) = 5


The proper subsets when 1 element is selected are:

{8} {15} {28} {41} {60}



Selecting any 2 elements from the 5 possible choices = 10 subsets possible

C(5,2) = 5! / 2! (5 - 2)!

C(5,2) = (5*4*3*2*1) / 2*1*3*2*1

C(5,2) = 5*4 / 2

C(5,2) = 10

The proper subsets when any 2 elements are selected:

{8,15} {8,28} {8,41} {8,60} {15,28} {15,41} {15,60} {28,41} {28,60} {41,60}


Selecting any 3 elements from the 5 possible choices = 10 subsets possible

C(5,3) = 5! / 3! (5 - 3)!

C(5,3) = (5*4*3*2*1) /3*2*1*2*1

C(5,3) = 5*4 / 2

C(5,3) = 10

The proper subsets possible when any 3 elements are selected:

{8,15,28} {8,15,41} {8,15,60} {8,28,41} {8,28,60} {8,41,60} {15,28,41} {15,28,60} {15,41,60} {28,41,60}


Selecting any 4 elements from the 5 possible choices = 5 subsets possible

C(5,2) = 5! / 4! (5 - 4)!

C(5,2) = (5*4*3*2*1) / 4*3*2*1*1

C(5,2) = 5 / 1

C(5,2) = 5


The proper subsets when any 4 elements are selected:

{8,15,28,41} {8,15,28,60} {8,15,41,60} {8,28,41,60} {15,28,41,60}


all the possible subsets of { 8, 15, 28, 41, 60}

Improper Subsets = 1

Proper Subsets = 5 + 10 +10 + 5 = 30



The FINAL ANSWER:

The number of all possible subsets of { 8, 15, 28, 41, 60} = 31

These are:

Proper Subsets:

{8} {15} {28} {41} {60}

{8,15} {8,28} {8,41} {8,60} {15,28} {15,41} {15,60} {28,41} {28,60} {41,60}

{8,15,28} {8,15,41} {8,15,60} {8,28,41} {8,28,60} {8,41,60} {15,28,41} {15,28,60} {15,41,60} {28,41,60}

{8,15,28,41} {8,15,28,60} {8,15,41,60} {8,28,41,60} {15,28,41,60}

Improper Subset:

{ 8, 15, 28, 41, 60}





Thanks for writing.
Staff

www.solving-math-problems.com



Jan 17, 2012
All Possible Subsets of a Set
by: Staff


Part I

Question:

by J Galyon
(California)

List all the subsets of { 8, 15, 28, 41, 60}


Answer:

First, some definitions:

SUBSET:

A subset contains at least one of the elements the set. For example, { 8} and { 15, 60} are both subsets of { 8, 15, 28, 41, 60}.

IMPROPER SUBSET:

An improper subset contains ALL the elements of the set. { 8, 15, 28, 41, 60} is the improper subset of {8, 15, 28, 41, 60}.

PROPER SUBSET:

A proper subset contains one or more of the elements the set, but not all the elements. For example, { 8} and { 15, 60} are proper subsets of { 8, 15, 28, 41, 60}.


ELEMENTS in a set or subset CAN BE LISTED MORE THAN ONCE without changing the set or subset.

For example, { 8, 8, 8} and { 15, 60, 60} are still proper subsets of { 8, 15, 28, 41, 60}.


ELEMENTS in a set or subset CAN BE LISTED IN ANY ORDER without changing the set or subset.

For example, { 8, 15, 28, 41, 60} and { 60, 8, 28, 41, 15} are the same set, even though the elements are not listed in the same order.


------------------------------------

Now for your question: List all the subsets of { 8, 15, 28, 41, 60}

Improper Subset = 1: { 8, 15, 28, 41, 60}

Proper Subsets = 30:

To find the number of proper subsets, you must determine how many COMBINATIONS (not permutations) of the elements 8, 15, 28, 41, and 60 are possible when you select 1 element, 2 elements, 3 elements, or 4 elements (you cannot select all 5 elements because that would be an improper subset, which you have already accounted for).

There is a formula which you can use to calculate these combinations (again, not permutations, but combinations):

C(n,r) = n! / r! (n - r)!

0 ≤ r ≤ n.

n = number of elements ( = 5)

r = number of elements selected (= 1, 2, 3, or 4)

Order is not important

Repetition is not allowed


---------------------------------------


Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com