Question

invalid,I think this is possible. I know all arguments in tfl with tautologies as conclusions are valid. I know a valid argument can't have a contradiction as a conclusion. But this is throwing me a bit. If it always evaluates to false, then it is inavlid automatically right?

Answer 1

A valid inference in deductive logic guarantees the truth of its conclusion given the truth of the premises, while an invalid inference does not. The structure of a deductive argument determines its validity. A disjunctive syllogism is a valid argument form.

Step-by-step explanation:

A deductive inference is called a valid inference when its structure guarantees the truth of its conclusion given the truth of the premises. It is important to note that valid arguments have a form such that if the premises are true, then the conclusion must be true, but this does not mean the conclusion itself is true. Testing the validity of deductive inferences involves assuming the premises are true and determining whether the conclusion logically follows from them.

On the other hand, an invalid inference does not guarantee the truth of the conclusion even if the premises are true. In other words, we cannot determine whether the conclusion is true or false based on the structure of an invalid inference. In order to prove an argument invalid, we can provide a counterexample where the premises are true but the conclusion is false. This counterexample demonstrates that the argument does not hold logically.

In the case of a disjunctive syllogism, where the argument is of the form 'X or Y, Not Y, Therefore X', if the premises are true, the conclusion must also be true. Therefore, this argument is valid. However, if an argument always evaluates to false, it is considered invalid automatically.