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

Fractions, a boy is six months old his sister was given birth to three mont...

a boy is six months old his sister was given birth to three month after him. if their cousin is 0.33years old, arrange their ages in ascending order

Explain mixed numbers with examples, Explain Mixed Numbers with examples? ...

Explain Mixed Numbers with examples? Everybody loves a bargain, right? But sometimes these "special deals" aren't what they seem to be. For example, pretend you were at a

Sequencing model, theory about solving sequencing problem using graphical m...

theory about solving sequencing problem using graphical method

Lisa was assigned 64 pages how many more pages must she read, Lisa was assi...

Lisa was assigned 64 pages to read for English class. She has ?nished of the assignment. How many more pages must she read? If Lisa has read 3/4 of the assignment, she has 1/4

Quick help for exam preparation, can you help me with entrance exam for uni...

can you help me with entrance exam for university ? i really need help so quick

Describe adding and subtracting square roots, Describe Adding and Subtracti...

Describe Adding and Subtracting Square Roots? To add or subtract square roots, the radicands must be the same. If the radicands are the same, add/subtract the coefficients (the

Example of factor by grouping, Factor by grouping each of the following. ...

Factor by grouping each of the following. 3x 2 - 2x + 12x - 8 Solution           3x 2 - 2x + 12x - 8 In this case we collect the first two terms & the final two te

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