Logic Sentences

Introduction to logic sentences

       In mathematical logic, a sentence is a predicate logic and a well formed formula with no free variables. A sentence is viewed by some as expressing a proposition. It makes an the assertion, potentially concerning any structure of L. This assertion has a fixed truth value with respect to the structure. In contrast, the truth value of a formula (with free variables) may be indeterminate with respect to any structure. As the free variables of an formula can range over several values (which could be members of a universe, relations or functions), its truth value may vary. And now let us see about the  logic sentences.(Sources – Wikipedia).


Basic Concept of Logic sentences:


      Logic is a set of sentences in a proper language. The logic sentences forms a  theory are called its theorems. Logic involved in statements or propositions

Five Terms Propositional in  logic sentences

Not
Or
And
If… then
If  and only if

Some Operations in Logic sentences:


Negation (˜p): The proposition is true means then  they can change into negative and vice versa.

Disjunction (pvq): The  two of the propositions are negative then the result is false or else true.

Conjunction (p^q): The  two of the propositions are right means then the result is true or else false.

Conditional (p→q): The Truth of the proposition ‘p’ is enough to truth of proposition ‘q’.

Bi-conditional (p↔q): ‘p’ is enough condition for ‘q’. ‘q’ is required for ‘p’. if not ‘q’ not ‘p’. Not ‘p’ unless ‘q’. Not ‘p’ without ‘q’.


Example problems:


Example 1:

A, B, can represent the  Logical sentences.  They represent some  definite propositions.

For example:

  A = "My shirt is white"

  B = "The sun is Hot"

 Now we get the final result are:

(A -> B)

But, if I were to dye my shirt  for white on a Hot day, then the

Sentence (A -> B) would become negative.

 Now the a logical sentence, such as:

  (A -> B)

 as discuss in above is true under some situation, and false under

other situation.

 By distinguish, the logical argument:
A |- B

 is *always* invalid.


Example 2:

What is the conjunction equation for the following statements?

     P: Peter reading story book.

     Q: Jenny reading newspaper.   

Solution:

     Given statement is as follows,

         P: Peter reading story book.

        Q: Jenny reading newspaper.   

    Conjunction is a ‘and’ declaration. The symbol of ‘and’ condition is ^.

    We can write the above statement in the following format.

      " Peter reading story book adn Jenny reading newspaper".   

     So logical equation = P ^ Q.

Example 3

Write the logical form for the following statement.

"Jenifer likes apples or oranges".

Solution:

      Let P:Jenifer likes apples

             Q:Jenifer likes oranges.

      The 'or' condition represents the disjunction.

       So logical form=PvQ.

Example 4

What is the conditional form for the following statements?

  "If we go to the college early, then we can enter the class room without punishment".

Solution:

     Given statement is as follows,

          P: If we go to the college early

         Q: then we enter the class room without punishment.

    Conditional is an ‘if-then’ declaration. The symbol of ‘if-then’ condition is ‘→’.

      So logical equation = P → Q.

Example 5

What is the logic form for the following statements?

 "Alex drives a bike or car".

Solution:

     Let P: Alex drives a bike.

          Q: Alex drives a car.

     The given declaration is ‘or’. The notation of ‘or’ is v.

     Therefore the logical form=PvQ.


Practice problems:


Question 1:

What is the conjunction form of the following statements?

     “ Peter has bicycle and bike”.

Question 2:

Write the logic form for the following statement?

    “Jessie likes to play tennis or badminton”.

Question 3:

What is the logic form for the following statement?

  "If u go to school then u will learn the english".

Answers:

1. Conjunction= P^Q

2. Disjunction =PvQ

3. Form =P→Q

These logic design questions are used to learn about the concepts.

What Is Numeric

Introduction to Numeric :

The term numeric can be referred to as numbers especially the characters from 0 to 9.It is a concept derived from 0 and the units. It can be represented as a quantity or it is related to the susceptible of all measurement. It is having the power of apparently denoting or naming .Numerical values are symbols as shown below

Numerals are  0,1,2,3,4,5,6,7,8,9.

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Analysis on Numeric:


Any number is a concept. ‘One’ is a number expressed in name and we use ‘1’ as numeral or symbol to denote it. Different types of symbols were used in various parts of the world to denote the numerals in past days. Number Pattern is defined as a list of numbers which would follow a certain rule.

Numerical pattern revolves all around the numeric values. None of these languages has a separate number system, hence these letters were instead also attributed a number. So we have to learn some knowledge on number pattern.

Some of the different types of number patterns are as follows:

Arithmetic sequence

Geometric sequence

Fibonacci sequence

Overview of Numeric type:

Types of numeric include following types,

Integer numeric

Approximate or floating-point numeric

Exact numeric

Basic operations of the numeric data types:

Minimum:

It is used to yield numerically smallest of the value. The general form is given as Min[x1, x2].

Example:

Minimum of particular numbers Min [3, 10]

Ans: 3

Maximum:

It is used to yield numerically biggest of the value. The general form is given as Max[x1, x2].

Example:

Minimum of particular numbers Max [87,140]

Ans: 140

Total:

The total type of data which is used to provides the whole value or sum of a particular list

Example:

Total [{A, B, C, D}]

Ans: A+B+C+D.

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Example problems:


Problem 1:

Find the minimum value for the given data 1, 8 using numeric data type.

Solution:

Minimum = Min [1, 8]

= 1

Problem 2:

Find the maximum value for the given data set [121, 28] using numeric data type.

Solution:

Maximum = Max [121, 28]

= 121

Problems 3:

Find the total for the following values, A, B, C using numeric data type.

Solution:

Total [{A, B, C}] = A+B+C.

Problems 4:

Find the total for the following values, 2, 3, 4, 5 using numeric data type.

Solution:

Total [{2, 3, 4, 5}] = 2+3+4+5 = 14

Study Velocity

Introduction to study velocity:-

• The study velocity of an object in an interval of time is the distance traveled by the object divided by the interval of time. the instantaneous speed is the limit of the standard speed as the duration of the time interval approaches zero.

• But study the distance(d) and the time taken(t) is given, the speed can be calculated using the following formula:

Velocity (V) = Distance / Time taken

• During this article to study velocity given distance, we are going to study some of the problems concerned in solving the study velocity if the distance is given.

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Example problems for study velocity:-


1) Solve the Velocity of an object which travels 244 meters in 18 seconds.

Solution:-

Distance = 244 m

Time = 18 sec

Velocity = Distance / Time taken

= 244 / 18

= 13.55 m/sec.

2) Solve the Velocity of an object which travels 320 meters in 20 seconds.

Solution:-

Distance = 320 m

Time = 20 sec

Velocity = Distance / Time taken

= 320 / 20

= 16 m/sec.

3) Solve the Velocity of an object which travels 458 meters in 42 seconds.

Solution:-

Distance = 458 m

Time = 42 sec

Velocity = Distance / Time taken

= 458 / 42

= 10.90 m/sec.

4) Solve the Velocity of an object which travels 322 meters in 34 seconds.

Solution:-

Distance = 322 m

Time = 34 sec

Velocity = Distance / Time taken

= 322 / 34

= 9.47 m/sec.

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Practice problems to study velocity:-


1) Solve the Velocity of an object which travels 315 meters in 13 seconds.

Answer: 24.23 m/s

2) Find the Velocity of an object which travels 252 meters in 18 seconds.

Answer: 14 m/s

3) Find the Velocity of an object which travels 186 meters in 8 seconds.

Answer: 23.25 m/s

4) Find the Velocity of an object which travels 112 meters in 4 seconds.

Answer: 28 m/s.

Vertices in Math

Introduction to Vertices in math
Vertex usually way a bend otherwise an end point wherever lines are congregate. Such as a square include four corners, each one is called a vertex. The plural formation of vertex is described as the vertices. For example the square contains four vertices. Vertices also a triangle would contain 3 vertices.


Vertices in math


Vertices in graph

Within math, a graph is a theoretical illustration of a position of things wherever a few pair of the things is related by links. The interrelated things are stand for by arithmetical concept called vertices, also the links to attach a few pairs of vertices be call edges. Usually, a graph is described within illustrative appearance like a place of points used for the vertices, connected through lines or else arc designed for the edges.

The ends might be directed otherwise undirected. for instance, condition the vertices symbolize people on a party, also here be an edge with two people but they vibrate hands, after to this be an undirected diagram, since condition person 1 vibrate hand through person 2, after that person 2 to vibrate hands through person 1.

In graph the vertices are as well describe points.


Vertices in angles

Vertices are measurement of angles. An angle is finished through the relating of two waves.

To relation be calling the vertex.

Angles are able to as well happen on the joint of two lines.

After to the point of joint is a vertex. These points are significant within the creation of an angle as well as also within the identification of an angle. Condition the vertex is on Point D, also it be the simply angle on Point D, the angle be able to be name Angle D.

Vertices are division of polygons. Every point of relationship is a vertex.

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Example 1: Solve the coordinates of the following equation

y=x^2+18x+20

Solution:

y=x^2+18x+20

dy/dx = 2x + 18

At vertex dy/dx = 0

2x + 18 = 0

x = -9

Therefore, y = (-9) ^2 + 18(-9) + 20 = 81- 162 + 20 = -56

Vertex contain co-ordinates (-9, -56)

Example 2: Solve the coordinates of the following equation

y=x^2+6x+2

Solution:

y=x^2+6x+2

dy/dx = 2x +6

At vertex dy/dx = 0

2x +6 = 0

x = -3

Therefore, y = (-3) ^2 + 6(-3) + 2 = 9- 18 + 2 = -7

Vertex contain co-ordinates (-3, -7)

Math Help Gateways

Introduction to math help gateways:

Math help gateways are websites that help students to learn math. Tutor vista is one of the best website which act as a gateway and help students in solving their homework problems and clear their doubts. This article for math help gateways covers the solving algebraic equation with step by step. After viewing this article student understand the concept and prepared well from math help gateways.


Math help gateways:


Example 1:

Find the value of the expression 12x+7 , if x= 4

Solution:

Substitute x = 4 in the given expression 12x + 7

12x + 7 = 12(4) + 7

= 48+ 7

X  = 55

Here the value of the expression is 55.

Example 2:

Solve: 2x - 2 = 38

Solution:

Given, 2x - 2 = 38

2x = 38 + 2

2x = 40

x = `40/2`

or    x = 20

Example 3:

Solve the following system:

x + y = 14 - (1)

4x - y = 11 - (2)

Solution:

Solve the (1) equation

y =14 -x

substitute in (2)equation

4x - (14 - x)=11

4x - 14 + x=11

5x=25

x=5

substitute value of x in (1)equation

5 + y=14

y=9

The solution is, (5, 9).

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Math help gateways:


Example 4:

One seventh of a certain number is 17. find out certain number.

Solution:

let the unknown value be x. one seventh of x is `( 1/7 ) * x`

so,  `( 1/7 ) * x` = 17

x = 17 * 7

x = 119

the number is  119.

Example 5:

If four times of a number is equal to 10. Then find what exactly the number is?

Solution:

let us assume the unknown number as " X "

Given   4 * X = 10.

Move left side term to right

Then          X = `10/4`

The unknown number x is

X = 2.5

Example 6:

Given :

12x - 2(7x-10x+2)+x.

Solution:

First simplify those brackets. So we multiply (7x-10x+2) with 2

So, 14x - 20x + 4

It can be written as 12x - 14x + 20x - 4 + x.

add the like terms

So,answer is (19x - 4)

Math Words A to Z

Introduction to math words a to z:

Understanding the concept of math is critical in this modern world today.  Math is used every day by all, from lay persons to degree professionals. Situations in which math is used differ from merely complementary a checkbook or calculating the sum of change due from a store transaction all the way to creating blueprints for an office building or house and the construction of those buildings. Understanding how to solve math is an easy way. Math words a to z has a mathematical terms from a to z.


Some mathematical terms from a to m– math words a to z.


Adjacent angles `–` adjacent angles are angles which are adjacent o each other and it shares a common vertex.

`Addition of vectors` – It is adding two vectors and the result is known as resultant vector.

Bisect – Bisection is dividing the given figure into two parts which are equal to each other.

Center – Center is a middle part of a geometric figure.

Cuboid – Cuboid is a rectangular box.

Decahedron – Decahedron is a three dimensional figure in which it has twelve faces.

Edge – An edge is a line segment between two vertices.

Finite – Limited number of elements.

Geometric sequence – Geometric sequence is a sequence of numbers in which second number is the multiplication of first number and any other constant and it goes on.

Horizontal axis – x axis is a horizontal axis because it is horizontal

Infinite – Unlimited number of elements

Identity matrix – Identity matrix is a square matrix in which all the diagonal elements are equal to 1 and the non diagonal elements are equal to zero.

Joint proportional – It is same as Joint variation.

Kite – It is geometric figure with four sides.

Linear equation – An equation which has only one degree.

Mass – Mass is a weight of an object.

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Some mathematical terms from n to z– math words a to z.


Number line – a line which has numbers from –infinity to +infinity.

Opposite angles – Angles which are opposite to each other.

Polynomial – Polynomial is a term in which it has a combination of variables, constants and exponents.

Quadrangle – Quadrilateral can also be say as quadrangle.

Rate of change – A change in y coordinate the change in x coordinate.

Secant – A straight line which cuts two or more points on a curve.

Tangent – Tangent is a straight line which touches a point on a circle.

Unequal – Two or more quantities are not equal to each other.

Variable – It is a letter used to refer unknown values.

Width – one of the side of a rectangle.

X – Intercept – value of x when y=0

Y-intercept – value of y when x=0

Zero product – A product of two or more expressions is equal to zero.

These are the some math words a to z.

Examples Integers Math

Introduction for examples integers in math:

The integers are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (-1, -2, -3, ...). Viewed as subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... -2, -1, 0, 1, 2, ...}. For example, 65, 7, and -756 are integers; 1.6 and 1½ are not integers. The set of all integers is often denoted by a boldface Z, which stands for Zahlen

-Source Wikipedia


Number Line for examples integers in math :


The number line is shown with the integers in ascending order from left to right:

|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|

-5    -4   -3   -2   -1    0    1    2    3    4    5

The integers on right sided to the 0 is positive integers and the integers on left side to the 0 is negative integers


Absolute Values for examples integers in math :


The absolute value of a number n is written as |n|. The absolute value of the numbers always be positive

Examples:

|44| = 44

|0| = 0

|-44| = 44


Rules for examples integers in math:


Addition rule:

Positive + Positive = Positive:

Negative + Negative = Negative:

In the addition of a negative and a positive number we have to subtract and place the largers number's sign.

Subtraction rules:

Negative - Positive = Negative

Positive - Negative = Positive + Positive = Positive

Negative - Negative = Negative + Positive

In the subtraction of a negative and a positive number we have to subtract and place the largers number's sign

Multiplication rules:

Positive x Positive = Positive

Negative x Negative = Positive

Negative x Positive = Negative

Positive x Negative = Negative

Division rules:

Positive ÷ Positive = Positive

Negative ÷ Negative = Positive

Negative ÷ Positive = Negative

Positive ÷ Negative = Negative

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Example problems for integers in math:


Addition Operation:

5 + 5 =10

5 + (-6) = 5 - 6 = -1

-6 + 5 = -1

Subtraction Operation:

5 - 5 = 0

6 - 5 = 1

5 - (-6) = 5 + 6 =11

-6 - (-6) = -6 + 6 = 0

Multiplication Operation:

6 *  6 = 36

-6 *  -6 = 36

-6 *  -6 = -36

6 *  -6 = -36

Division Operation:

6`-:` 6 = 1

-6 `-:` -6 = 1

-6`-:` 6 = -1

6 `-:` -6 = -1