subset - A is a subset of B if all elements of the set A are elements of the set B

A set has a cardinality of 9. How many proper subsets does the set have?

A set has a cardinality of 9. How many proper subsets does the set have?
The set has 2^9 = [B]512 proper subsets[/B]

Determine if the statement below is True or False

Determine if the statement below is True or False
If B ? A, then A ? B = B
Is this statement True or False?
[B]True:[/B] If B ? A, then B ? A
So A ? B is the similar elements of both. B contains itself as a subset.
So this is [U]true[/U]

Find the subset of {a,b,c,d,e}

Find the subset of {a,b,c,d,e}
Using our power set calculator, we find [URL='https://www.mathcelebrity.com/powerset.php?num=a%2Cb%2Cc%2Cd%2Ce&pl=Show+Power+Set+and+Partitions']all the 32 subsets of {a,b,c,d,e}[/URL]

Permutations and Combinations

Calculates the following:

Number of permutation(s) of n items arranged in r ways =_{n}P_{r}

Number of combination(s) of n items arranged in r__unique__ ways = _{n}C_{r} including subsets of sets

Number of permutation(s) of n items arranged in r ways =

Number of combination(s) of n items arranged in r

power set for S= {b,c,f}

power set for S= {b,c,f}
The [I]power set[/I] P is the set of all subsets of S including S and the empty set ?.
Since S contains 3 terms, our Power Set should contain 2^3 = 8 items
[URL='https://www.mathcelebrity.com/powerset.php?num=b%2Cc%2Cf&pl=Show+Power+Set+and+Partitions']Link to power set for this problem[/URL]
P = [B]{{}, {b}, {c}, {f}, {b,c}, {b,f}, {c,f}, {b,c,f}}[/B]

Set Notation

Given two number sets A and B, this determines the following:

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J_{σ}(A,B)

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A