Sets and its types

Sets are major concepts in mathematics that is taught in the middle school. In general terms, sets mean collection. A set is a collection of things, letters, words and more. For example: building block , puzzle, construction toys etc. can be termed as a set of kids’ educational toys. Let’ have a closer observation of sets in mathematics.

Sets: Any collection of things that can be grouped under one category is called as a set. For example: {Lego building block , Megabloks building blocks, Fisher Price building blocks, Peacock building blocks}. This is a collection of kids' building blocks and therefore a set. Sets can be classified into different types. Let’s have a look at the same in this post.

Finite Sets: A finite set is a type of set that consist a finite number of elements. For example: {kids laptop online, kids’ mobile online, kids’ electronic toys online}. This is a finite set of electronics for kids that include elements like kids’ laptop online and so on.

Infinite Sets: An infinite set is a type of set that consist infinite number of elements. For example: {1, 2, 3, 4, 5…..}. Here, the set consist infinite numbers and therefore is an infinite set.
Null Sets: A null set is a type of set that consists nothing. Null sets are also referred as empty sets or void sets.  A null set is denoted by {} or Ø.

Unit Sets: A unit set is a type of set that consist only one element. Unit sets are also referred as singleton sets or one point sets. For example: { baby food appliances }. Here, the set is a unit set as it consist only one element that is baby food appliances.
Find the type of sets for the below sets:
• {1, 2, 3, 4, 5} = Finite Set
• {} = Null Set
• {Barbie doll} = Unit Set
• {0, 1, 2, 3, 4, 5….} = Infinite Set
These are the basics about sets in mathematics.

Definition Value Proposition

Definition of proposition

Proposition is a statement which is either true or false. There are some statements which appear to be true and false at the same time. "The area of a circle is `pi`r2   ". , is a statement or proposition whose value is true. " 6 is an odd integer" is another proposition whose value is false. Consider the question " how are you? ". This is not a proposition since it does not possess a truth value. " What time is it now ?" is another example which is not  a proposition. Propositions are usually denoted by lower case letters like p, q, r, s etc.
Truth Value of a Proposition:

Proposition are statements which are either true or false. The statements which appear to be both at the same time are called paradoxes. For example consider the statement " I am a liar ". If this statement is true, then the speaker cannot be a liar. So the statement is false. If the statement is false then what the speaker says is false.Therefore the speaker is not a liar!

If a proposition is true, we say that the truth value of the proposition is True, denoted by T.

If a proposition is false, then we say that the truth value of the proposition is False, denoted by F.
Negation of a Proposition(definition Value Proposition)

" Mathematics is easy " is a  proposition.  Now, consider the proposition " Mathematics is not easy ". If the former is true, then the latter is false and vice-versa. Here the second proposition is called the negation of the first proposition. If p is a proposition, then the negation is denoted by the symbol ~p. The truth values of p and ~p are as follows :

p           ~p

T             F

F             T
Compound Propositions and Connectives

A combination of two or more propositions is called a compound proposition. There are four connectives used to make compound propositions. They are summarised below.

Compound proposition            connective                 symbol

Conjunction                                 and                               `^^`

Disjunction                                   or                                  `vv`

Conditional                                  if...then                          `|->`

Biconditional                               if and only if                   `harr`

High Line Construction

The line is a geometrical object in math and it is used for other shape construction. We can define the line by its properties. The single point is basis for high visible line construction. We can state the direction by line and it is straight. Now we are going to see about high line construction.
Explanation for High Line Construction

The high line in math:

The line is high symmetric and it is differentiated from other shapes by properties. The properties are straight, infinitely long, infinitely thin, zero width and the line is indicating the distance of two points.

High line construction:

We can construct the line easily and the parameters for line is simple one. Three types of geometry tools are used in high line construction. The tools are,

Pencil
Ruler
Protractor

What are all the steps followed in high line construction?

We should draw the line in white paper.
Take the pencil and sharpen the tip.
Start the line construction by dot and the line length is measured.
We are taking the line measurement in centimeter or millimeter.
The length is starting with dot till the length end point.
The ruler is used for measurement.
And joining the points with ruler.
Finally, we got the parallel line.
We can draw the perpendicular line by protractor and the angle mark and the starting point is joined.
The direction of line is represented with arrow mark in graph.
The arrow mark also indicated as the line is infinite length.
The construction of other shapes also done by line as basic tool.

More about High Line Construction

How to draw a line?

high line construction

The high visible line is drawn with ruler measurements like cm and mm. The mm value is represented as decimal values that is 6. 8 cm. Here the 8 is a mm value.

Pendulum Length

The length of the pendulum in the clock can be found by knowing the angle between the maximum points of the pendulum and the distance covered by the pendulum. The length of the pendulum can be calculated using the arc length formula where the known values are the central angle and the distance covered by the pendulum between the maximum points. In the following article we will see in detail about the topic pendulum length.

pendulum
More about Pendulum Length:

The pendulum oscuillstes from a single point and the pendulum covers a maximum position on the each side and the angle between the maximum positions can be measured and the distance covered by the pendulum between the maximum positions is also measured. Using all the values and substituting these values in the arc length formula we can calculate the length of the pendulum from the formula.

The formula for the arc length L = (theta/360)*2*pi*r

Here the θ is the angle between the maximum positions and r is the length of the pendulum and L is the distance covered by the pendulum between the maximum positions.
Example Problems on Pendulum Length:

1. The angle covered between the maximum positions of pendulum and the distance covered between the maximum positions are 110 degrees and 20 cm. Find the length of the pendulum.

Solution:

The length of the pendulum = (360*L)/(2*pi*theta)

= (360*20)/(2*pi*110)

= 360/11*pi

= 10.4 cm

2. The angle covered between the maximum positions of pendulum and the distance covered between the maximum positions are 120 degrees and 25 cm. Find the length of the pendulum.

Solution:

The length of the pendulum = (360*L)/(2*pi*theta)

= (360*25)/(2*pi*120)

= (3*25)/(2*pi)

= "12 cm"
Practice problems on pendulum length:

1. The angle covered between the maximum positions of pendulum and the distance covered between the maximum positions are 100 degrees and 18 cm. Find the length of the pendulum.

Answer: 10.3 cm.

Quadrilaterals Kite Tutor

The students are learn mathematics by using tutoring in online.  The tutor and students are communicated and the tutor share the information about related topics in online. The kites are quadrilaterals because it is drawn in geometry with four sides. The quadrilaterals have convex property in all types. So the kites also has convex property. Now we are going to learn about quadrilaterals kite by tutor.

Explanation for Quadrilaterals Kite Tutor

Tutor description for kite quadrilateral:

The quadrilateral kite has two pair of equal sides. So it is also known as deltoids. The adjacent sides are present next side. The parallelogram is a regular polygon. The kite also regular polygon.

The kite quadrilaterals property:

The right angle measurement is based on diagonals intersection.

The adjacent sides angles are equal.

The area of kite is find out by half of the diagonals product.

The perimeter of kite is find out by sum of length.

Quadrilaterals kite formula:

Area based on diagonals method – `(d_(1)d_(2))/2` .
Area based on trigonometry method – ab sin C.
Perimeter based on side’s sum – 2a + 2b.

More about Quadrilaterals Kite Tutor

Example problems for quadrilaterals kite tutor:

Problem 1: Calculating the kite area with diagonals 5.1 cm and 6.3 cm.

Tutor solution:

The diagonals of quadrilateral kite are d1 = 5.1 cm and d2 = 6.3 cm.

The area of quadrilaterals kite is `(d_(1)d_(2))/2` = `(5.1 * 6.3)/2` = 16 cm2.

Problem 2: Calculating the quadrilateral kite perimeter with  length of sides 21 cm and 10.8 cm.

Tutor solution:

The length of sides are a = 21 cm and b = 10.8 cm.

The quadrilateral kite perimeter is 2a + 2b = 2 x 21 + 2 x 10.8 = 63.6 cm.

I am planning to write more post on how to solve a math word problem and Matrix Solver . Keep checking my blog.

Exercise problems for quadrilaterals kite tutor:

1. The quadrilaterals kite with diagonals 14 cm and 12.5 cm. Calculating the kite area.

Tutor solution: The quadrilateral kite area is 87.5 cm2.

2. Calculating the kite perimeter with sides 18.3 cm and 13.8 cm.

Tutor solution: The kite perimeter is 64.2 cm.

Fixed Rate Calculator

A loan in which the interest rate do not alter through the whole expression of the loan reverse of adjustable rate A loan in which the interest rate does not modify through the whole term of the loan for an entity taking out a loan when rates are low, the fixed rate loan would permit him or her to "lock in" the short rates and not be worried with fluctuations. On the another hand, if interest rates were in the past elevated at the time of the loan, he or she would profit from a floating rate loan, since as the prime rate cut down to historically normal levels, the rate on the loan would reduce. Reverse of adjustable rate. A calculator is a small electronic device; it is used to achieve the fundamental operations of arithmetic. Modern calculators are more convenient than computers, while most PDAs are similar in size to handheld calculators.

Fixed rate calculator
Examples for the Fixed Rate Calculator:
Fixed rate calculator – Example 1:

Determine the payments and interest for a fixed rate loan, using monthly interest compounding and monthly payments. The purchase price $150, no of monthly payments is 2 months, and interest rate 5.000%, and the payment calculator computes the payment amount for you.
Solution:

Fixed rate calculator

The down payment amount is $11.00

The Loan amount is $ 139.00

Payment amount is $ 69.93

Interest rate is      5.000 %

Interest compounding: Monthly

Total amount financed: $139.00

Total payments: $139.87

Total finance charge: $0.87

Payment schedule:

Date           Payment InterestPrincipal Balance

Loan     08-26-2010                            139.00

1           09-26-2010   69.93       0.58    69.35    69.65

2           10-26-2010   69.94       0.29    69.65

2010 Total                139.87      0.87

Grand Total              139.87      0.87
More Examples for the Fixed Rate Calculator:
Fixed rate calculator – Example 1:

Determine the payments and interest for a fixed rate loan, using monthly interest compounding and monthly payments. The purchase price $100, no of monthly payments is 5 months, and interest rate 5.000%, and the payment calculator computes the payment amount for you.
Solution:

Fixed rate calculator

The down payment amount is $18.02

The Loan amount is $ 89.00

Payment amount is $ 18.02

Interest rate is      5.000 %

Interest compounding: Monthly

Total amount financed: $89.00

Total payments: $90.11

Total finance charge: $1.11

Payment schedule:

Event      Date             Payment Int    PrincipalBalance

Loan       08-26-2010                          89.00

1             09-26-2010  18.02    0.37    17.65  71.35

2             10-26-2010  18.02    0.30    17.72  53.63

3             11-26-2010  18.02    0.22    17.80  35.83

4             12-26-2010  18.02    0.15    17.87  17.96

2010 Total                  72.08    1.04    71.04

5             01-26-2011  18.03    0.07    17.96

2011 Total             18.03    0.07    17.96

Grand Total            90.11    1.11

Score as in Mathematical Terms

“Score” means 20! .The term "score" was came from the old English word “scoru”. It is the Middle age English word. Also, in turn, it came from the Norse skor. In mathematical terms score carried a value 20. Abraham Lincoln's celebrated Gettysburg consists of the phrase, "Four score and 7 years ago". In bible the term mentioned as “three score years and ten”.

Orgin of score:

In mathematical terms "Scores" way "groups of 20", just as "dozens" way "groups of 12". "Score" is eventually from the Proto-Indo-European root (s)ker-, sense "to cut" . Another English offspring is "shear". English still uses the word "score" to submit to an indentation or line made by a sharp instrument. Scores cut in wooden tally firewood were used in including, a fact we still make the unwitting suggestion to today when we talk regarding "keeping score". For a while in the history of the Germanic languages, the word for the cut used to record the number 20 became a word for the number itself.
Examples

4 score

Score mean 20 in mathematical terms

`4xx20=80`

Therefore four score is 80

3 score and 10

Score mean 20 in mathematical terms

`3 x 20` and 10

60+10=70.

Therefore 3 score and 10 is 70.

In Abraham Lincoln's celebrated Gettysburg consists of the phrase, "Four score and 7 years ago".

The phrase denotes, in mathematical terms

`4xx20` and 7

80+7

87

The phrase means 87 years ago.

Three score difference 10

Three score

`3xx20`

60 difference 10

60-10

50

Some mistakes arises that in some cases score is taken as 10. It wii lead to wrong answer

We cant assume any value to score. It means to 20 alone.

I am planning to write more post on Calculate Density  Keep checking my blog.

Related examples like score:

Like score there are a lot of examples are in mathematical terms.

Foursquare

It means symmetrical in all dimensions or equal in all dimensions like cubical.

Like the words numbers also holds some meaning, Let take an example

223

It bibbiblically mean things involving to an order of survival beyond the visible, demonstrate-able space; that which is above and away from the laws of nature; and/or matters concerning the stroke or influence of the ghostly or psychic powers and the top-secret knowledge of them.