cardinality - a measure of the number of elements of the set

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]

D= {a,b,c,d,e,f,g} the cardinality of set D is

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

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]}

Please help!!

(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

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

Sets

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 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”.

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]