Question

"He is a golden retriever, therefore he is a dog." Try to create a propositional calculus for the previous statement where you: affirm the antecedent, affirm the consequent, deny the antecedent, and deny the consequent. Think about which are valid and which are invalid.

o Affirm the antecedent: This is a golden retriever, therefore this is a dog (true)
o Affirm the consequent: This is a dog, therefore this not a golden retriever (false)
o Deny the antecedent: This is not a golden retriever, therefore this is not a dog (false
o Deny the consequent: This is not a dog, therefore this is not a golden retriever (true)

Answer 1

Affirming the antecedent and denying the consequent are valid inferences, while affirming the consequent and denying the antecedent are fallacies in propositional calculus.

Step-by-step explanation:

In propositional calculus, affirming the antecedent means affirming that if the antecedent is true, then the consequent is also true. For example, if we affirm that something is a golden retriever, we can conclude that it is a dog. This is a valid inference as it follows the logical form of modus ponens. Affirming the antecedent is a valid inference in propositional calculus.

On the other hand, affirming the consequent is invalid. If we affirm that something is a dog, we cannot conclude that it is a golden retriever. This is because there can be other dog breeds as well. Affirming the consequent is a fallacy in propositional calculus.

Denying the antecedent is also invalid. If we deny that something is a golden retriever, we cannot conclude that it is not a dog. There can be other dog breeds as well. Denying the antecedent is a fallacy in propositional calculus.

Denying the consequent is a valid inference in propositional calculus. If we deny that something is a dog, we can conclude that it is not a golden retriever. This is a valid inference as it follows the logical form of modus tollens. Denying the consequent is a valid inference in propositional calculus.