Which of the following statements are true? (A) An argument is sound when it…

Concept: Validity is a property of an argument’s form — an argument is valid exactly when it is impossible for all of its premises to be true while its conclusion is false. Truth, by contrast, is a property of the individual statements. Soundness joins the two: a sound argument is a valid argument whose premises are all in fact true. So validity is fixed by the premise-to-conclusion relation alone, and never by the actual truth value of any single statement taken by itself.

Application: Testing each of the four statements against that concept:

• Statement (A) — “sound = valid and only true premises” restates the standard definition of soundness exactly, so it is true.

• Statement (B) — a conclusion can be true in an argument whose premises lend it no support at all, so the conclusion’s truth cannot by itself establish validity. This statement is false.

• Statement (C) — consider: “All whales are fish; all fish are mammals; therefore all whales are mammals.” The form is valid (it is a standard universal-syllogism form), both premises are false, and the conclusion is true. So this statement is true.

• Statement (D) — consider: “All whales are fish; all fish are birds; therefore all mammals are warm-blooded.” Nothing in the premises supports the conclusion, so the argument is invalid, yet its premises are false and its conclusion is true. So this statement is true.

Cross-check: The one combination validity rules out is all-true premises together with a false conclusion. Every other pairing of premise truth and conclusion truth is available to valid and invalid arguments alike:

This also shows why (B) fails: a true conclusion sits in both the valid and the invalid rows, so it carries no information about validity on its own.

Result: Statements (A), (C) and (D) are true and statement (B) is false, so the true set is (A), (C) and (D).