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

Levels of significance - rejection and acceptance regions, Levels of signif...

Levels of significance A level of significance is a probability value which is utilized when conducting tests of hypothesis. A level of significance is mostly the probability

Calculus with vector functions - three dimensional space, Calculus with Vec...

Calculus with Vector Functions In this part we need to talk concisely on derivatives, limits and integrals of vector functions. Like you will see, these behave in a quite pred

Melissa is four times if jim is y years old, Melissa is four times as old a...

Melissa is four times as old as Jim. Pat is 5 years older than Melissa. If Jim is y years old, how old is Pat? Start along with Jim's age, y, because he appears to be the young

To find out the perimeter of a triangular give formula, To find out the per...

To find out the perimeter of a triangular region, what formula would you use? The perimeter of a triangle is length of surface a plus length of side b plus length of side c.

To calculate volume of cylinder which formula is used, Mimi is filling a te...

Mimi is filling a tennis ball can along with water. She wants to know the volume of the cylinder shaped can. Which formula will she use? The volume of a cylinder is π times the

Transportation problem, matlab code for transportation problem solved by vo...

matlab code for transportation problem solved by vogel''s approximation method

Quadratic equation, can anyone explain me the concept of quadratic equation...

can anyone explain me the concept of quadratic equation?

Inside function and outside function, "Inside function" and "outside functi...

"Inside function" and "outside function : Generally we don't actually do all the composition stuff in using the Chain Rule. That can get little complexes and actually obscures the

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