# math

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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.

• math -

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

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