math
posted by heatherly .
Indicate whether the deductive reasoning used is an example of affirming the hypothesis or denying the conclusion.
8 If a number is divisible by 3, then the sum of the digits of that number is divisible by 3.
The sum of the digits of a number is not divisible by 3. Therefore the number is not divisible by 3.

It is a case of denying the conclusion.
Let
A=a number is divisible by 3
B= the sum of the digits of that number is divisible by 3
The hypothesis is
If A > B
A case of affirming the hypothesis (modus ponendo ponens):
126 is divisible by three, therefore the sum of its digits is divisible by three.
A case of denying the consequence (modus tollens):
The sum of the digits of 17 is not divisible by three, therefore 17 is not divisible by 3.
See
http://en.wikipedia.org/wiki/Modus_ponens
http://en.wikipedia.org/wiki/Modus_tollens