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

How to raise powers of monomials, How to raise Powers of Monomials ? To ...

How to raise Powers of Monomials ? To raise a monomial to a certain power: Step 1: Place the entire monomial inside parentheses, and place the desired power outside the paren

Determine the widest piece of mail, A mailbox opening is 4.5 inches high an...

A mailbox opening is 4.5 inches high and 5 inches wide. Determine the widest piece of mail able to ?t in the mailbox without bending? a. 9.5 inches b. 2.2 inches c. 6.7 in

How many baseball cards does peter now have, Peter purchased 14 latest base...

Peter purchased 14 latest baseball cards for his collection. This increased the size of his collection through 35%. How many baseball cards does Peter now have? First, you must

Dimensional analysis, Rachel had 3.25 quart of ice tea. her family drank 9 ...

Rachel had 3.25 quart of ice tea. her family drank 9 cups.How many cups are left

Define markov process, Define Markov process. Markov process is one in...

Define Markov process. Markov process is one in which the future value is independent of the past values, given the current value

Math, what is 24566x12567=

what is 24566x12567=

Multiplication of complex numbers, Multiplication of complex numbers Af...

Multiplication of complex numbers After that, let's take a look at multiplication.  Again, along with one small difference, it's possibly easiest to just think of the complex 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