Indicate whether the deductive reasoning used is an example of affirming the hypothesis or denying the conclusion.
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.
The fallacy of affirming the hypothesis is based on the following hypothesis:conclusion set
If A then B, IF B then A.
The fallacy of denying the conclusion is
If A, then B; If NOT B, then NOT A
Does that help?
If you are teaching Math, the way to teach these is to demonstrate with Venn Diagrams, in my opinion. STudents understand spacial arguments better than written logic.
The deductive reasoning used in this scenario is an example of denying the conclusion.
To understand why, let's break it down:
1. The first statement, "If a number is divisible by 3, then the sum of the digits of that number is divisible by 3," is the hypothesis.
2. The second statement, "The sum of the digits of a number is not divisible by 3," is the evidence or observation.
3. The conclusion drawn from the evidence is, "Therefore the number is not divisible by 3."
By denying the conclusion, the deductive reasoning is challenging the initial hypothesis based on the observation that the sum of the digits is not divisible by 3. This form of reasoning aims to disprove the hypothesis by showing a counterexample.