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November 9, 2008

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of ‘Logical reasoning’. The mini-lessons here include: Getting started, Conditionals,Converse, Inverse, Biconditional and Contrapositive, Inductive and Deductive Reasoning, Disproving Statements.

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- Mathematics > Geometry

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of ‘Logical reasoning’. The mini-lessons here include: Getting started, Conditionals,Converse, Inverse, Biconditional and Contrapositive, Inductive and Deductive Reasoning, Disproving Statements.

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting started - Graphing a linear equation.

In this mini-lesson we introduce a linear equation, which basically is an equation whose graph is a line. For example, x + y - 2 = 0. Once we know the basics of linear equations, we'll move on to more advanced topics such as rearranging an equation to draw its graph, and to determine its slope and intercepts.

In this mini-lesson we introduce a linear equation, which basically is an equation whose graph is a line. For example, x + y - 2 = 0. Once we know the basics of linear equations, we'll move on to more advanced topics such as rearranging an equation to draw its graph, and to determine its slope and intercepts.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting Started - Logical reasoning.

This mini-lesson; with the help of some examples, defines and deals with a statement, truth value, negation, postulate and theorem. This might seem complicated here in text, but once you have instructor explain it to you in their voice and handwriting in the video, it will be fairly easy for you to understand. You should remember that the main idea behind logical reasoning is to use the information and preconditions to make a conclusion. You will find that a variety of conditions and you must use an "if"-"then" approach. To work the solution you should read the whole problem, and choose the best hint or clue before starting.

A statement is a declarative sentence which is either true or false, but not both. The truth value refers to whether or not something is true or false. E.g. the truth value of a statement is T if it is true and F if it is false (the statement ‘2 + 3 = 5’ has truth value T). The negation is usually constructed by adding or removing “not” from the statement and it is symbolically, ~p, or p, e.g. If p is "I have a job", then ~p is "I do not have a job". While postulate is a proposition that is accepted as true in order to provide a basis for logical reasoning, a theorem is a statement that has been proven, or can be proven, from the postulates.

This mini-lesson; with the help of some examples, defines and deals with a statement, truth value, negation, postulate and theorem. This might seem complicated here in text, but once you have instructor explain it to you in their voice and handwriting in the video, it will be fairly easy for you to understand. You should remember that the main idea behind logical reasoning is to use the information and preconditions to make a conclusion. You will find that a variety of conditions and you must use an "if"-"then" approach. To work the solution you should read the whole problem, and choose the best hint or clue before starting.

A statement is a declarative sentence which is either true or false, but not both. The truth value refers to whether or not something is true or false. E.g. the truth value of a statement is T if it is true and F if it is false (the statement ‘2 + 3 = 5’ has truth value T). The negation is usually constructed by adding or removing “not” from the statement and it is symbolically, ~p, or p, e.g. If p is "I have a job", then ~p is "I do not have a job". While postulate is a proposition that is accepted as true in order to provide a basis for logical reasoning, a theorem is a statement that has been proven, or can be proven, from the postulates.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Conditionals.

This section will help to understand how do you write the statements as a conditional. Conditionals are 'if-then' statements. More precisely, conditionals are statements that say if one thing happens, another will follow. E.g. Statements such as "I have a job." may be replaced by*p* and the conditional statement, "If I have a job, then I must work." might be replaced by *p**q*, where *q* in this case is equivalent to "I must work".

It is also explains with the help of some examples, how to identify the hypothesis and the conclusion of a conditional and write its truth value. To represent an if-then statement symbolically, let*p* represent the hypothesis and *q* represent the conclusion. Then we have the basic form of an if-then statement shown below:

If*p* then *q*

*p* = hypothesis *q* = Conclusion

For example, in the conditional “If point*D* is between point *C* and *E*, then *CD* + *DE* = *CE*”, the statement “point *D* is between point *C* and *E*” is a hypothesis and “*CD* + *DE* = *CE*” is a conclusion.

This section will help to understand how do you write the statements as a conditional. Conditionals are 'if-then' statements. More precisely, conditionals are statements that say if one thing happens, another will follow. E.g. Statements such as "I have a job." may be replaced by

It is also explains with the help of some examples, how to identify the hypothesis and the conclusion of a conditional and write its truth value. To represent an if-then statement symbolically, let

If

For example, in the conditional “If point

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Converse, Inverse, Biconditional and Contrapositive.

In this mini-lesson you'll learn with the help of some examples, the definition and basics of converse, inverse, biconditional and contrapositive of a conditional. This might seem complicated here in text, but once you have instructor explain it to you in their voice and handwriting in the video, it will be fairly easy for you to understand.

The converse of a conditional is formed by interchanging the hypothesis and the conclusion.

Statement: if*p*, then *q*

Converse: if*q*, then *p*

i.e.*q* ? *p*. E.g. for the conditional “If a polygon is a hexagon, then the polygon has exactly six sides”, the converse is “If a polygon has exactly six sides, then the polygon is a hexagon”.

The inverse of a conditional is formed by negating the hypothesis and the conclusion i.e. ~*p* ? ~*q*. E.g. the conditional, “If you serve imported sparkling water, then you have good taste” has the inverse, “If you do not serve imported sparkling water, then you do not have good taste”. It should be easy to see that the converse of the inverse is the contrapositive. For example, the converse of *p*q is *q**p* and the inverse of *p*q is ~*p*~*q*.

If a conditional and its converse are both true, they can be combined into a single statement by using the words “if and only if”. The statement that contains the words “if and only if” is called a bioconditional. Its basic form is;

*p* if and only if *q*. i.e. *p* *q*.

E.g. the biconditional statement “*x* + 5 = 12, “if and only if” *x* = 7”.

The contrapositive of a conditional is a new conditional with the hypothesis and conclusion interchanged and the hypothesis and conclusion both negated i.e. ~*p* ? ~*q*. E.g. the conditional, “if two lines are parallel, then they do not intersect” has the contrapositive, “if two lines intersect, then they are not parallel.”

In this mini-lesson you'll learn with the help of some examples, the definition and basics of converse, inverse, biconditional and contrapositive of a conditional. This might seem complicated here in text, but once you have instructor explain it to you in their voice and handwriting in the video, it will be fairly easy for you to understand.

The converse of a conditional is formed by interchanging the hypothesis and the conclusion.

Statement: if

Converse: if

i.e.

The inverse of a conditional is formed by negating the hypothesis and the conclusion i.e. ~

If a conditional and its converse are both true, they can be combined into a single statement by using the words “if and only if”. The statement that contains the words “if and only if” is called a bioconditional. Its basic form is;

E.g. the biconditional statement “

The contrapositive of a conditional is a new conditional with the hypothesis and conclusion interchanged and the hypothesis and conclusion both negated i.e. ~

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

Member Rating

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Inductive and Deductive Reasoning.

Here you'll learn; with the help of video and instructor’s hand writing, about two basic types of reasoning called inductive and deductive reasoning. ‘Inductive Reasoning’ is the process of observing data, recognizing patterns, and making generalizations from the observations. The generalization used in inductive reasoning is called a conjecture. ‘Deductive Reasoning’ is the process of demonstrating that if certain statements are accepted as true, then other statements can be shown to follow from them. Both are important to understand as Geometry often deals with proofs and proofs are based on logical reasoning which follow these two basic types.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

Here you'll learn; with the help of video and instructor’s hand writing, about two basic types of reasoning called inductive and deductive reasoning. ‘Inductive Reasoning’ is the process of observing data, recognizing patterns, and making generalizations from the observations. The generalization used in inductive reasoning is called a conjecture. ‘Deductive Reasoning’ is the process of demonstrating that if certain statements are accepted as true, then other statements can be shown to follow from them. Both are important to understand as Geometry often deals with proofs and proofs are based on logical reasoning which follow these two basic types.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Disproving Statements.

In this section, with the help of some examples, you will learn to use logical reasoning to prove statements that are true and find counter examples to disprove statements that are false.

A statement and its converse say different things. In fact, some true statements have false converse. An ‘if-then’ statement is false, if an example can be found for which hypothesis is true and conclusion is false. Such an example is called a counter example. E.g. the statement “The perimeter of a rectangle can never be an odd number of units.” You know that the perimeter of rectangle is given by 2(*l* + *w*), where *l* is the length and *w* is the width of the rectangle. Let us take the values of *l* = 7units and *w* = 1.5 units, substitute 7 for *l* and 1.5 for *w* in above formula i.e. 2(7 + 1.5), which gives 17. Therefore, this example is disproving the statement “The perimeter of a rectangle can never be an odd number of units.”

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this section, with the help of some examples, you will learn to use logical reasoning to prove statements that are true and find counter examples to disprove statements that are false.

A statement and its converse say different things. In fact, some true statements have false converse. An ‘if-then’ statement is false, if an example can be found for which hypothesis is true and conclusion is false. Such an example is called a counter example. E.g. the statement “The perimeter of a rectangle can never be an odd number of units.” You know that the perimeter of rectangle is given by 2(

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