logic 1.4

Is it possible to have a valid argument that is also sound?

yes An argument is both valid and sound if the conclusion follows with necessity from the premises, and the argument's premises are all true.

Suppose you have a deductive argument with a true conclusion. Given this information, what do you know about the soundness of this argument?

The argument may be either sound or unsound. If a deductive argument has a true conclusion, the argument may be either sound or unsound. According to the definition of "soundness," a sound argument must be valid, and its premises must all be true. If these two criteria are not both met, then the argument is unsound. But having a true conclusion does not settle this question, because it doesn't tell us anything about the truth of the premises. In fact, some arguments that have a true conclusion are sound, while others are unsound.

Suppose you have an argument with true premises and a true conclusion. Given this information, what do you know about the validity of this argument?

The argument may be either valid or invalid. If an argument has true premises and a true conclusion, the argument may be valid or invalid. Even though the premises and conclusion may all be true in an argument, the argument is only valid if the premises necessitate or guarantee that the conclusion could not be false. Therefore, an argument with all true premises and a true conclusion could be either valid or invalid, depending upon whether the premises necessitate that the conclusion must be true.

Suppose you have a valid argument with all false premises. Given this information, what do you know about the argument's conclusion?

The conclusion could be either true or false. From the fact that the argument is valid, all you know is that it is impossible for the premises to be true and the conclusion to be false. But the possibility of having this set of truth values is already eliminated by the false premises (that is, you cannot have all true premises). So, the truth value of the conclusion will not affect the validity. Thus, if an argument is valid with all false premises, the conclusion could be either true or false.

Suppose you have an invalid argument with a true conclusion. Given this information, what do you know about the premises of this argument?

The premises may be any combination of true and false. If an invalid argument has a true conclusion, you do not have enough information to determine whether the premises are true or false. All that you know of the argument is that it is possible for the premises to all be true and the conclusion to be false. But if the conclusion is true, then any other combination of actual truth values for the premises is consistent with this definition of "invalidity."