What is inductive reasoning, Mathematics

Assignment Help:

What is Inductive Reasoning ?

Sometimes we draw conclusions based on our observations. If we observe the same results again and again, we conclude that the event always has the same outcome. We call this kind of reasoning inductive reasoning. We call a conclusion arrived at through inductive reasoning as a generalization.

1322_Inductive Reasoning.png

Example 1 :  Suppose there are 3 differently shaped triangles. If we cut off the corners of each of the triangles and patch them together, we will find that the sum of the angles of each triangle is 180°. If we do this to a large number of triangles, then we find that the sum is always 180°. We can generalize this to say that the sum of the angles of a triangle is 180°.

1955_Inductive Reasoning 1.png

Example 2 : Here we have two right triangles and find and2092_Inductive Reasoning 2.png and 1714_expression.png We can generalize this to say: The side opposite the right angle of a triangle is the longest side.

Sometimes generalizations can be false. We look for counterexamples to show a generalization is false.

Example 3 :  Generalization: If a quadrilateral has four congruent sides, it has four congruent angles.
Counterexample: We can draw a quadrilateral with four congruent sides but with unequal angles to show this is a false generalization.

163_expression 1.png


Related Discussions:- What is inductive reasoning

HELP, a manufacturer is interested in developing a benefit segmentation of ...

a manufacturer is interested in developing a benefit segmentation of the cameramarket.suggest some major benefit segments with market targeting strategies.

Integration, It is known that a radioactive material decays at a rate propo...

It is known that a radioactive material decays at a rate proportional to the amount present.If after a period of 12 years,a 2g piece of radium weighs 1.99g.How long will it be befo

Kurtosis-measure of central tendency, Kurtosis - It is a concept, whic...

Kurtosis - It is a concept, which refers to the degree of peakedness of a described frequency distribution. The degree is generally measured along with reference to general di

Determine the centralizer and the order of the conjugacy, Determine the cen...

Determine the centralizer and the order of the conjugacy: 1)      Determine the centralizer and the order of the conjugacy class of the matrix [1, 1; 0, 1] in Gl­ 2 (F 3 ).

Polynomials, give an example of a binomial of degree 27?

give an example of a binomial of degree 27?

Differentiate product rule functions, Differentiate following functions. ...

Differentiate following functions. Solution At this point there in fact isn't a lot of cause to use the product rule.  We will utilize the product rule.  As we add

Why is the steepness of a curve partially calculate, Can you explain why is...

Can you explain why is the steepness of a curve partially calculated by the units of measurement?

Circle, prove that - there is one and only one circle passing through three...

prove that - there is one and only one circle passing through three non - collinear points

Debate over answer to an equation..., The math equation is written exactly ...

The math equation is written exactly this way: 0+50x1-60-60x0+10=??? The answer I get is 10 and others say 0 0+50=50 50x1=50 50-60=-10 -10-60=-70 -70x0=0 0+10=10

Functions, The figure shows the sketch graphs of the functions

The figure shows the sketch graphs of the functions

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd