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

Find a formula for its frequency of oscillation, The frequency of oscillati...

The frequency of oscillation of an object suspended on a spring depends on the stiffness k of the spring (called the spring constant) and the mass m of the object. If the spring is

Describe least three characteristics at medieval world, Based upon the prim...

Based upon the primary sources, describe at least three characteristics that mark the early modern world as distinctly different than the Medieval world that preceded it. You might

Indicestitle.., Advantages and disadvantages of paasche indices

Advantages and disadvantages of paasche indices

Determine if the three vectors lie in similar plane or not, Determine if th...

Determine if the three vectors a → = (1, 4, -7), b → = (2, -1, 4) and c → = (0, -9, 18) lie in similar plane or not. Solution Thus, as we noted prior to this example al

Write down two more reasons why division is difficult, Write down two more ...

Write down two more reasons why children consider 'division' difficult. Regarding the first reason given above, one of fie few division related experiences that the child perhaps d

First order linear differential equation, Newton's Second Law of motion, wh...

Newton's Second Law of motion, which recall from the earlier section that can be written as: m(dv/dt) = F (t,v) Here F(t,v) is the sum of forces which act on the object and m

Distance and Section Formulae, find the coordinates of points of tri-sectio...

find the coordinates of points of tri-section of the line joining the points (-3,0) and (6,6).

Finding absolute extrema of f(x) on [a, Finding Absolute Extrema of f(x) on...

Finding Absolute Extrema of f(x) on [a,b] 0.   Confirm that the function is continuous on the interval [a,b]. 1.  Determine all critical points of f(x) which are in the inte

Show that af+bd+ce=ae+bf+cd= 1/2 , In figure, the incircle of triangle ABC...

In figure, the incircle of triangle ABC touches the sides BC, CA, and AB at D, E, and F respectively. Show that AF+BD+CE=AE+BF+CD= 1/2   (perimeter of triangle ABC), Ans:

Calculate time interval, From top of a tower a stone is thrown up and it re...

From top of a tower a stone is thrown up and it reaches the ground in time t1. A second stone is thrown down with the same speed and it reaches the ground in t2. A third stone is r

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