element - an element (or member) of a set is any one of the distinct objects that belong to that set. In chemistry, any substance that cannot be decomposed into simpler substances by ordinary chemical processes.

12.66 g of calcium are heated in air,17.73 g of calcium oxide is formed.The percent oxygen in the co

12.66 g of calcium are heated in air,17.73 g of calcium oxide is formed.The percent oxygen in the compound is?
17.73g Calcium oxide - 12.66g Calcium = 5.07g Oxygen
Mass of the element / Mass of the compound * 100%
= 5.07g O / 17.73g CaO2 X 100%
= 28.6% of Oxygen in the compound
[B][U]Check Your Work [/U][/B]
Mass of the element / Mass of the compound X 100%
= 12.66g Ca ÷ 17.73g CaO2 X 100%
= 71.4% Ca
71.4% Ca + 28.6% O = 100% CaO2

A belongs to Both X and Y

A belongs to Both X and Y
What this means is Element A belongs to Set X and Set Y.
We write this as follows
A is an element of X is written as A ? X
A is an element of Y is written as A ? Y
[B]A ? X & A ? Y[/B]
[FONT=Droid Serif][COLOR=rgb(34, 34, 34)][SIZE=14px][/SIZE][/COLOR][/FONT]

A U ? = A

A U ? = A
Let x ? [I]S[/I], where [I]S[/I] is the universal set.
First we show that if A ? Ø ? A.
Let x ? A ? Ø.
Then x ? A or x ? Ø. by definition of the empty set, x cannot be an element in Ø.
So by assumption, x ? A ? Ø, x must be in A.
So A ? Ø ? A.
Next, we show that A ? A ? Ø.
This is true because the set resulting from the union of two sets contains both of the sets forms the union
Since A ? Ø ? A and A ? A ? Ø, we have that A ? Ø = A.

All the colors of the rainbow

All the colors of the rainbow
You can find this with the acronym: ROYGBIV
[LIST=1]
[*][B]Red[/B]
[*][B]Orange[/B]
[*][B]Yellow[/B]
[*][B]Green[/B]
[*][B]Blue[/B]
[*][B]Indigo[/B]
[*][B]Violet[/B]
[/LIST]
[U]Written as a set, we have 7 elements:[/U]
{[B]Red, Orange, Yellow, Green, Blue, Indigo, Violet[/B]}

Combinations with Replacement

Calculates the following:

How many combinations can we have from a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed?

How many combinations can we have from a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed?

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 elements on the principal diagonal of matrix B

Find the elements on the principal diagonal of matrix B
Matrix B:
|0 0 8|
|-1 3 0|
|2 -5 -7|
The main diagonal is any entry where row equals column
|[B]0[/B] 0 8|
|-1 [B]3 [/B] 0|
|2 -5 [B]-7[/B]|
In this case, it is [B]0, 3, -7[/B]

If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.

If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.
We know from set theory that:
n(A U B) = n(A) + n(B) - n(A ? B)
Plugging in our given values, we get:
n(A U B) = 90 + 125 - 35
n(A U B) = 180
The problem asks for n(A U B)'. This formula is found with:
n(A U B)' = n(U) - n(A U B)
n(U) is the universal set which is 250, so we have:
n(A U B)' = 250 - 180
n(A U B)' = [B]70[/B]

Let A={a,b,c} and B={1,2,3} Compute A?B

Let A={a,b,c} and B={1,2,3} Compute A?B
Union means all elements in either A or B, so we have:
A?B = [B]{a,b,c,1,2,3}[/B]

Molar Mass

Calculates the molar mass of an element or solution.

Periodic Table Items

Shows details of all the elements on the periodic table including atomic weight, natural state.

Permutations with Replacement

Calculates the following:

How many permutations can we have from a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed?

How many permutations can we have from a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed?

Set B is the set of distinct letters in the word GIFT

Set B is the set of distinct letters in the word GIFT
Set B has 4 elements below:
B = [B]{G, I, F, T}[/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

Set of all consonants in the word,'SECONDARY'

Set of all consonants in the word,'SECONDARY'
Our set has 6 elements below:
[B]{C, D, N, R, S, Y}[/B]

set of all continents

set of all continents
Our set of 7 elements is below:
{[B]Africa, Antarctica, Asia, Australia/Oceania, Europe, North America, and South America[/B].}

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.

States that begin with the letter C

States that begin with the letter C
Our set has 3 elements:
[B]{California, Colorado, Connecticut}[/B]

The average of 171 and x?

The average of 171 and x?
The phrase [I]average[/I] means add up all the items in the number set, divided by the count of items in the number set.
Our number set in this case is {171, x} which has 2 elements. Therefore, our average is:
[B](171 + x)/2[/B]

The planets in the solar system as set G

The planets in the solar system as set G.
Since Pluto was removed as a planet, we have the following set G with 8 elements:
G = [B]{Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}[/B]

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]

Write in set builder form {all possible numbers formed by any two of the digits 1 2 5}

Write in set builder form {all possible numbers formed by any two of the digits 1 2 5}
With 3 numbers, we got [URL='https://www.mathcelebrity.com/factorial.php?num=3!&pl=Calculate+factorial']3! = 6[/URL] possible numbers formed by the two digits
[LIST=1]
[*]12
[*]15
[*]21
[*]25
[*]51
[*]52
[/LIST]
In set builder notation, we write this as:
{x : x ? {12, 15, 21, 25, 51, 52})
x such that x is a element of the set {12, 15, 21, 25, 51, 52}

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of rolling these two dice, given that the red die shows an even number and the green die shows an odd number greater than 1?
[LIST]
[*]Red Die Sample Space {2, 4, 6}
[*]Green Die Sample Space {3, 5}
[*]Total Sample Space {(2, 3), (2, 5), (4, 3), (4, 5), (6, 3), (6, 5)}
[*]The sie of this is 6 elements.
[/LIST]