Explain Geometry
So what is the difference between Inductive and Deductive reasoning? It is really quite simple. There are several reasons why they are different.
The first is that Deductive uses logic, while Inductive deals with patterns. This is the most basic reason. A more complex reason is that Deductive, when properly applied, cannot be disproven, when Inductive can. Deductive reasoning is based on upon theorems or facts. Deductive reasoning uses 1 fact applied to a given idea, and uses multiple other theorems or facts to come to a conclusion. This method of reasoning is always solid, because it can easily be proven over and over again, unless you use an incorrect theorem.
Example of Deductive Reasoning:
If 2 segments are congruent, then they have the same length. AB is congruent to XY.
Therefore AB is equal to XY.
Inductive reasoning, on the other hand, is based on patterns. A theory proven by inductive reasoning is truly only as long as a counterexample that has not been found. It can be proven over and over again, but one example of a fact that says otherwise makes the theory untrue. A more detailed example, the scientific method, we will examine in the elaborate section. A proof by inductive reasoning, can always be disproven, and can sometimes never fully be considered to be a fact.
Example of Inductive Reasoning:
1/3, 2/4, 3/5...Find the next number
It is 4/6
However, in some instances of inductive reasoning, this may not be the case because of error in the understanding of the pattern, it's complexity, or insufficient data. For example:
1,2,3,5...
The next number could be either 7 or 8, depending on whether the pattern is prime numbers, or the Fibonacci sequence.
This is the big difference. Deductive reasoning is using facts and is completely true, if the logic is true, while Inductive reasoning is based on patterns and, while it can be fairly certain of, is never fully proven.
EXPLAIN!
1) A math student first hypothesizes that the number of a polygon = (n-2)180 degrees. n equals the number of sides. This student proves this statement to be true.
A) Give some examples when the student was using inductive reasoning?
B) Give some examples when the student using deductive reasoning?
**Be sure to explain your thinking!!
After writing your response, move on to ELABORATE!