6/9 6. Testing Arguments with Truth Tables Free Online FlashCards

What makes a deductive argument valid?

An argument is valid when no possible case makes all its premises true and its conclusion false.

What is a sound argument?

An argument is sound when it is valid and all of its premises are true.

When is a conditional false?

A conditional is false only when its antecedent is true and its consequent is false.

How many rows do two basic propositions require?

With two basic propositions, a complete truth table has $2^2=4$ rows.

What is a valuation?

A valuation is one assignment of truth values to the basic propositions.

What is the joint-premise form for two premises?

For premises $P_1$, $P_2$, and conclusion $C$, construct $(P_1 \land P_2) \to C$.

What truth-table result establishes validity?

The argument is valid exactly when the joint-premise conditional is a tautology: true on every row.

What is a countervaluation?

A countervaluation is a row where every premise is true and the conclusion is false.

Does a false premise on some row prove invalidity?

No. Rows with false premises do not refute validity; only a row with all premises true and a false conclusion does.

Is $p \to q,\ p, \therefore q$ valid?

Yes. The form $p \to q,\ p, \therefore q$ is valid because no valuation makes both premises true and $q$ false.

Is $p \to q,\ q, \therefore p$ valid?

No. If $p=F$ and $q=T$, both premises are true while the conclusion $p$ is false.

How can you search quickly for invalidity?

Set the conclusion to F, then try to make every premise T. If the assignments are consistent, they form a countervaluation.