Question 248852: Decide whether the argument is an example of inductive or deductive reasoning.
37 + 19 = 56, 7 + 29 = 36, 41 + 7 = 48. The sum of two prime numbers is even.
Found 3 solutions by stanbon, chosenpoint, Alan3354:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! It is inductive because you are using
a couple of examples to arrive at a
general statement.
---------
Deductive would state a general priciple
and then state some consequences.
----------------
Cheers,
Stan H.
Answer by chosenpoint(26)  (Show Source):
You can put this solution on YOUR website! ******EDITED TO ADD THE FOLLOWING:******
******As tutor Alan3354 pointed out, 2 is a prime number, so the following deductive reasoning works for all prime numbers except 2. It was not a complete proof, just an idea of the difference between inductive and deductive reasoning. I will edit the statement/answer below.******
To quickly follow up on this,
We can use deductive reasoning in the following manner (this is NOT a complete proof, just an example of deductive reasoning).
As the other tutor stanbon said in the original answer, inductive reasoning is based on examples, deductive reasoning is based on the general case!
Let x be any prime number EXCEPT 2 (which by definition will be odd, since it can not have 2 as a divisor).
Let y be any prime number EXCEPT 2 (which can equal x, which will also be odd by definition).
Since the sum of 2 odd numbers will always be even (using properties of integers), the sum of 2 prime numbers will also then be even.
x + y = an even number
The sum of any 2 prime numbers will always be even, unless ONLY ONE of those prime numbers is 2. Of course if both of those prime numbers are 2, then you again have a sum that is an even number. :)
Answer by Alan3354(69443)  (Show Source):
|
|
|
