4.1.4. Rules of Inference

Try these first

1. 1.

   What is a valid argument?

   Hint

   Think about the logical connection between premises and conclusion.

2. 2.

   List one rule of inference.

   Hint

   Which rule tells us about affirming the conclusion?

3. 3.

   What does Modus Ponens allow us to conclude?

   • p → q
   • q
   • ¬p

   Hint

   Look for the conclusion drawn from true premises.

4. 4.

   True or False: If p → q and ¬q, then it can be concluded that ¬p.

   • True
   • False

   Hint

   Think about which statements are negated.

5. 5.

   Using both Modus Ponens and Modus Tollens, construct a reasoning chain where one leads to the other, ensuring all steps are logically valid.

   Hint

   Make sure to track your premises closely.

6. 6.

   Analyze the following argument for fallacies: 'If I eat ice cream (p), then I will be happy (q). I am happy (q); therefore, I ate ice cream (p)'. Identify any fallacies and correct the argument.

   Hint

   Consider alternate sources for the conclusion's truth.