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

Help, how long would it take if a submarine if it goes 3 feet per minute to...

how long would it take if a submarine if it goes 3 feet per minute to get to 20000 answer

Evaluate negative infinity, Evaluate both of the following limits. ...

Evaluate both of the following limits. Solution : Firstly, the only difference among these two is that one is going to +ve infinity and the other is going to negative inf

Linear equations, Linear Equations We'll begin the solving portion of ...

Linear Equations We'll begin the solving portion of this chapter by solving linear equations. Standard form of a linear equation: A linear equation is any equation whi

Unit Rates, I need help on how to do real word problm with unit rates.

I need help on how to do real word problm with unit rates.

Example for articulate reasons and construct arguments, A Class 4 teacher w...

A Class 4 teacher was going to teach her class fractions. At the beginning of the term she asked the children, "If you had three chocolates, and wanted to divide them equally among

Calculate the area of the skirt to the nearest foot, Pat is making a Christ...

Pat is making a Christmas tree skirt. She needs to know how much fabric to buy. Using the example provided, calculate the area of the skirt to the nearest foot. a. 37.7 ft 2

Maths, whats 100 + 90 - 6

whats 100 + 90 - 6

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