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

Heat loss in cylindrical pipe, which physics law is used to describe heat l...

which physics law is used to describe heat loss in cylindrical pipe

Two circles touching internally prove that ox:oy=oa:ob, Two circles touchin...

Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB. Given : Two circles touching internally a

Problem, La proporción de empleados de una empresa que usan su auto para ir...

La proporción de empleados de una empresa que usan su auto para ir al trabajo es 5:16. Si hay un total de 800 empleados, diga la cantidad de autos que se espera que haya estacionad

Whta is truth table, What is a truth table? Distinguish between Tautology &...

What is a truth table? Distinguish between Tautology & Contradiction?

ADDING AND SUBTRACTING EQUATION, GUESS THE NUMBER THAT WHEN YOU SUBTRACT 6 ...

GUESS THE NUMBER THAT WHEN YOU SUBTRACT 6 AND THEN SUBTRACT 0 IS-14

Cynthia, #stioquen..Store A is advertising a sale that will reduce prices o...

#stioquen..Store A is advertising a sale that will reduce prices on all merchandise by 15%. Store B is advertising a sale that will reduce prices on all merchandise by one over fiv

How many packets of the first type did she purchase, The manager of a garde...

The manager of a garden store ordered two different types of marigold seeds for her display. The first type cost her $1 per packet and the second kinds cost $1.26 per packet. How m

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