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.
This deductive reasoning is an example of denying the conclusion.
To understand why, let's break down the argument step by step:
1. Statement: If a number is divisible by 3, then the sum of the digits of that number is divisible by 3.
2. Observation: The sum of the digits of a number is not divisible by 3.
3. Conclusion: Therefore, the number is not divisible by 3.
In this reasoning, we start with a hypothesis (if a number is divisible by 3, then the sum of the digits is divisible by 3). We then observe that the sum of the digits is not divisible by 3. From that observation, we reach the conclusion that the number is not divisible by 3.
Since the reasoning is operating by observing the outcome (the sum of the digits not being divisible by 3) and inferring the conclusion (the number is not divisible by 3), it is an example of denying the conclusion.
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