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

Differentiate exponential functions, Differentiate following functions. ...

Differentiate following functions. (a)    R ( w) = 4 w - 5 log 9 w (b)   f ( x ) = 3e x + 10x 3 ln x Solution :  (a) It will be the only example which doesn't includ

Determine the exterior angle, Using the sketch below and the fact that ∠A +...

Using the sketch below and the fact that ∠A + ∠B + ∠C + ∠D = 325, Determine m∠E.   a. 81° b. 35° c. 25° d. 75° b. The addition of the measures of the exterio

Applying quadratics math question, A boat tour company charges $11 for a ha...

A boat tour company charges $11 for a harbour tour and averages 450 passengers on Saturdays. Over the past few months, the company has been experimenting with the price of a tour a

Marketing, What''s the price for a Marketing plan assignment ( postgraduate...

What''s the price for a Marketing plan assignment ( postgraduate)5000 words?

Cylinder, #question Show that the enveloping cylinder of the conicoid ax 2 ...

#question Show that the enveloping cylinder of the conicoid ax 2 + by 2 + cz 2 = 1 with generators perpendicular to the z-axis meets the plane z = 0 in parabolas

Basics of vectors - calculus, Vectors - The Basics Let us start this s...

Vectors - The Basics Let us start this section off with a quick discussion on what is the use of vector.  Vectors are utilized to present quantities that have both a magnitude

Convex rectilinear figure, the sum of the interior angles of a convex recti...

the sum of the interior angles of a convex rectilinear figure is equal to sum of the exterior angles. then the number of sides is

Find the Regular Grammar for the following Regular Expressio, Find the Regu...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

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