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]

D= {a,b,c,d,e,f,g} the cardinality of set D is Cardinality of D, denoted |D|, is the number of items in the set: |D| = [B]7[/B]

Months with 31 days as set M Our cardinality of this set is 7, as show below: {[B]January, March, May, July, August, October, December[/B]}

(1) |P(A)| = 4 <-- Cardinality of the power set is 4, which means we have 2^n = 4.[B] |A| = 2 [/B] (2) |B| = |A|+ 1 and |A×B| = 30 |B| = 6 if [B]|A| = 5[/B] and |A x B| = 30 (3) |B| = |A|+ 2 and |P(B)|−|P(A)| = 24 Since |B| = |A|+ 2, we have: 2^(a + 2) - 2^a = 24 2^a(2^2 - 1) = 24 2^a(3) = 24 2^a = 8 [B]|A |= 3[/B] To check, we have |B| = |A| + 2 --> 3 + 2 = 5 So |P(B)| = 2^5 = 32 |P(A)| = 2^3 = 8 And 32 - 8 = 24

Free 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 J_σ(A,B)
* Dice's Coefficient
* If A is a subset of B
* If B is a subset of A

Free Sets Calculator - This lesson walks you through what a set is, how to write a set, elements of a set, types of sets, cardinality of a set, complement of a set.

The set of all letters in the word p lus is The cardinality of this set is 4 with the elements below: [B]{p, l, u, s}[/B]

The set of months of a year ending with the letters “ber”. We build set S below: [B]S = {September, October, November, December}[/B] The cardinality of S, denoted |S|, is the number of items in S: [B]|S| = 4[/B]