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 FalseDetermine 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 CombinationsFree Permutations and Combinations Calculator - Calculates the following:
Number of permutation(s) of n items arranged in r ways = nPr
Number of combination(s) of n items arranged in r unique ways = nCr including subsets of sets
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 NotationFree Set Notation Calculator - 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 Jσ(A,B)
* Dice's Coefficient
* If A is a subset of B
* If B is a subset of A
