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

How to solve lim 1-cos(x)/1-cos(4x) as x tends to zero, Use L''hopital''s r...

Use L''hopital''s rule  since lim X-->0  1-cos(x)/1-cos(4x)  is in the indeterminate form 0/0 when we apply the limt so by l''hoptital''s rule differentiate the numerator and den

Find the third vertex of a triangle, Find the third vertex of a triangle if...

Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3).

Undetermined coefficients, In this section we will see the first method whi...

In this section we will see the first method which can be used to find an exact solution to a nonhomogeneous differential equation. y′′ + p (t ) y′ + q (t ) y = g (t) One of

Mr, i needed help with algebra

i needed help with algebra

Introduction to knowing your maths learner, INTRODUCTION : The other day I...

INTRODUCTION : The other day I overheard 6-year-old Ahmed explaining to his older sister about why swallowing the seeds of an orange is harmful. He said, "The seed will become a p

Draw the digraph for the partial order, 1. Consider the relation on A = {1,...

1. Consider the relation on A = {1, 2, 3, 4} with relation matrix: Assume that the rows and columns of the matrix refer to the elements of A in the order 1, 2, 3, 4. (a)

Minimizes the sum of the two distance, The value of y that minimizes the su...

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

The mean value theorem with proof, The Mean Value Theorem  Assume f(x)...

The Mean Value Theorem  Assume f(x) is a function that satisfies both of the subsequent. 1.   f(x) is continuous on the closed interval [a,b]. 2.   f(x) is differentiabl

Round 468.235 to the nearest hundredth, Round 468.235 to the nearest hundre...

Round 468.235 to the nearest hundredth ? The hundredths place is the second digit to the right of the decimal point (3). To decide how to round, you must like as at the digit t

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