A deductive argument is valid if :

Concept — Validity is a property of a deductive argument's FORM, not of the facts it happens to report. An argument is valid when the conclusion follows from the premises with necessity: it is impossible for all the premises to be true and the conclusion false at the same time. Validity therefore never claims that the premises are actually true; it only fixes what must happen to the conclusion when they are.

Application — read each offered truth-value combination against that definition.

1. Validity rules out exactly one combination: true premises together with a false conclusion. If an argument ever shows that pattern, its conclusion did not follow with necessity, so the argument is not valid.

2. When the premises are false, the definition promises nothing about the conclusion. A valid form can carry false premises to a true conclusion or to a false one, so neither false-premise combination states anything that validity delivers.

3. When the premises are true, the definition forces the conclusion to be true as well — true premises with a false conclusion is exactly what validity forbids. So the truth-value combination that a valid deductive argument delivers whenever its premises are true is: premises are true and conclusion is true. That is the combination this question asks for.

Cross-check — the same reasoning laid out over all four combinations:

Note — a truth-value combination by itself never proves that an argument is valid: an invalid argument can also happen to have true premises and a true conclusion, and a valid argument can rest on false premises. Validity is settled by the form of the argument, and formally it is defined negatively — an argument is valid unless true premises can accompany a false conclusion. What the true-premise, true-conclusion combination captures is the one thing validity does guarantee, which is why it is the accepted answer to this question. A valid argument whose premises are in fact true is called a sound argument.