Cengage 1.4 Aplia assignment

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

It is possible for the conclusion to be false.

Is it possible to have a sound argument that is not valid?

No Explanation: An argument cannot be both sound and invalid. Because validity is one criterion for soundness, if an argument is sound then it must also be valid.

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.

Suppose you have an argument with false premises and a true conclusion. What do you know about the validity of this argument?

The argument may be either valid or invalid.

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

The argument may be either valid or invalid. Explanation: If an argument has false premises and a false conclusion, then the argument may be either valid or invalid. To determine whether an argument is valid, you should first assume the premises are all true and then ask whether the conclusion would also have to be true. If the answer to this question is yes, then the argument is valid; if the answer to this question is no, then the argument is invalid. But knowing only that the premises and conclusion are both false does not give you enough information to answer this question one way or the other, because some arguments with false premises and a false conclusion are valid, while others are invalid. Thus, an argument with false premises and a false conclusion may be either valid or invalid, depending upon whether the premises would make the conclusion true any time they themselves were true.

Suppose you have a sound argument. Given this information, what do you know about the argument's validity?

The argument must be valid. Explanation: If an argument is sound, then the argument must also be valid. According to the definition of "soundness," for an argument to be sound, the argument must be valid and the argument must have premises that are all true. So if you know an argument is sound, then you know it must be valid also.

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

The conclusion could be either true or false. Explanation: If an argument is valid with some true premises and some false premises, 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 conclusion could be either true or false without affecting the validity of the argument. 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 false premises. Given this information, what do you know about the conclusion of this argument?

The conclusion may be either true or false. Explanation:If an argument is invalid with false premises, then you can draw no inference about the truth value of the argument's conclusion. If an argument is invalid, then you know that it is at least possible for the premises to be true and the conclusion to be false simultaneously (even though these may not be the actual truth values of the argument's statements). In an invalid argument, you can have false premises and a false conclusion, or false premises and a true conclusion. What matters for invalidity is that it would be possible to make the premises true and the conclusion false.

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

The conclusion must be true.

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

Yes