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Subsets of {mom, dad, son, daughter}











































Subsets of {mom, dad, son, daughter}

What would the subsets of this be?

Number of proper subsets = COMBINATIONS of the elements mom, dad, son, and daughter are possible.

This is the formula which you can use to calculate these combinations:

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

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Jan 23, 2012
Subsets of {mom, dad, son, daughter}
by: Staff


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Part II



Selecting any 1 element from the 4 possible choices = 4 subsets possible

n = number of elements ( = 4)
r = number of elements selected (= 1)

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

C(4,1) = 4! / 1! (4 - 1)!

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

C(4,1) = 4 / 1

C(4,1) = 4

The proper subsets when 1 element is selected are: {mom} {dad} {son} {daughter}


Selecting any 2 elements from the 4 possible choices = 6 subsets possible

n = number of elements ( = 4)
r = number of elements selected (= 2)

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


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

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

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

C(4,2) = 12 / 2

C(4,2) = 6

The proper subsets when any 2 elements are selected: {mom,dad} {mom,son} {mom,daughter} {dad,son} {dad,daughter} {son,daughter}


Selecting any 3 elements from the 4 possible choices = 4 subsets possible

n = number of elements ( = 4)
r = number of elements selected (= 3)

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

C(4,3) = 4! / 3! (4 - 3)!

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

C(4,3) = 24 / 6

C(4,3) = 4

The proper subsets possible when any 3 elements are selected: {mom,dad,son} {mom,dad,daughter} {mom,son,daughter} {dad,son,daughter}



all the possible subsets of { mom, dad, son, daughter }

Improper Subsets = 1

Proper Subsets = 4 + 6 + 4 = 14



The FINAL ANSWER:

The number of all possible subsets of { mom, dad, son, daughter } = 15

These are:

Proper Subsets:

{mom} {dad} {son} {daughter}

{mom,dad} {mom,son} {mom,daughter} {dad,son}
{dad,daughter} {son,daughter}

{mom,dad,son} {mom,dad,daughter} {mom,son,daughter} {dad,son,daughter}

Improper Subset:

{ mom, dad, son, daughter }



Thanks for writing.
Staff

www.solving-math-problems.com


Jan 23, 2012
Subsets of {mom, dad, son, daughter}
by: Staff


Part I

Question:

What would the subsets of this be?


Answer:

A subset contains at least one of the elements the set. For example, { mom } and { dad, son } are both subsets of { mom, dad, son, daughter }.

IMPROPER SUBSET:

An improper subset contains ALL the elements of the set. { mom, dad, son, daughter } is the improper subset of { mom, dad, son, daughter }.

PROPER SUBSET:

A proper subset contains one or more of the elements the set, but not all the elements. For example, { mom } and { dad, son } are proper subsets of { mom, dad, son, daughter }.


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

For example, { mom, mom, mom } and { dad, son, son } are still proper subsets of { mom, dad, son, daughter }.


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

For example, { mom, dad, son, daughter } and { son, mom, daughter, dad } are the same set, even though the elements are not listed in the same order.


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Subsets of {mom, dad, son, daughter}


Improper Subset = 1: { mom, dad, son, daughter }

Proper Subsets = 14:

To find the number of proper subsets, you must determine how many COMBINATIONS (not permutations) of the elements mom, dad, son, and daughter are possible when you select 1 element, 2 elements, or 3 elements (you cannot select all 4 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 ( = 4)

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

Order is not important

Repetition is not allowed


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