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

Using a number strip substract , Another aid that can help children pract...

Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means

Math, 3 9/10 into decimal

3 9/10 into decimal

Problem solving for andre, Problem solving for andre A can of powdered ...

Problem solving for andre A can of powdered milk and a can of evaporated milk cost Php 83.90 together. Two cans of evaporated milk and a can of powdered milk cost Php 118.05

What is the square root of -i, To find sq root by the simple step... root (...

To find sq root by the simple step... root (-i)=a+ib............... and arg of -i= -pi/2 or 5pi/2

Geometry, two sides of an equilateral triangle have lengths 3x-1 and 3x-1. ...

two sides of an equilateral triangle have lengths 3x-1 and 3x-1. Which of 27-x or 2x-4 could be the length of the third side?

Partial Differentiation, If the sides angles of a triangle ABC vary in such...

If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0

What is the probability of choosing a red ball, Q. What is the probability ...

Q. What is the probability of choosing a red ball? Ans. A box contains a red, blue and white ball. Two are drawn with replacement. (This means that one ball is selected, i

Calculate plurality based on the number of voters and candid, Consider an e...

Consider an election with 721 voters. A) If there are 5 candidates, at least x votes are needed to have a plurality of the votes. Find x. B) Suppose that at least 73 votes are n

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