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

Define symmetric, Define symmetric, asymmetric and antisymmetric relations....

Define symmetric, asymmetric and antisymmetric relations.    Ans: Symmetric Relation A relation R illustrated on a set A is said to be a symmetric relation if for any x,

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Hypothesis testing of the difference between proportions, Hypothesis Testin...

Hypothesis Testing Of The Difference Between Proportions Illustration Ken industrial producer have manufacture a perfume termed as "fianchetto." In order to test its popul

Which expression has an answer of 18, Which expression has an answer of 18?...

Which expression has an answer of 18? Use the order of operations and try every option. The first option results in 14 since 2 . 5 = 10, then 10 + 4 = 14. This does not work. T

Wants to Join as expert, Hi.. This is dinesh kumar I just joined experminds...

Hi.. This is dinesh kumar I just joined experminds.com , i wamt to receive assignment in maths and want to complete students assignment within time. Please help me how i can become

Shortcuts of fraction and squareroot, I am student of M.com and also doing...

I am student of M.com and also doing practice to crack bank or other competitive exam..please tell me shortcuts

Polynomials, On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if ...

On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.

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