2. Truth-Table Definition of Validity An argument is truth-table valid if it is impossible for the premises to all be True and the conclusion False. I.e., there is no line of the table on which all the premises are True and the conclusion is False.

3. Truth-table definition of Invalidity It is possible for all the premises to be True and the conclusion False. I.e. there is at least one line of the table on which the premises are all True and the conclusion is False

4. If Washington was beheaded then he’s dead. He is dead, so he must have been beheaded. W > D / D // W T T T T F F F T T F T F T F T F T T F F -- Invalid, because on line 3, the premises are all True, but the conclusion is False

5. It isn’t true that both Bill and Hillary Clinton were invited to Bush’s inaugural ball, therefore neither of them was. ~( B. H) // ~ (B v H) F T T T T T F F T F F T T F F F F T T T F T T F F F T T T F F F  Invalid because on line 3 The premise is T, but the conclusion is F.

6. Future presidents will be allowed to serve a third term only if the Twenty-second Amendment is repealed. That amendment will not be repealed, so future presidents will not be allowed to serve more than two terms. F > T / ~T // ~F T T T T F F F T T F T F F T T F F T T F F T F T T F T F Valid because on every line where both premises are true, the conclusion is also True

7. If the sun is a variable star, then its energy will drop drastically at some point in the future. If its energy drops drastically at some point in the future, the earth will become a giant iceball. Therefore if the sun is a variable star, the earth will become a giant iceball. V > D / D > I // V > I T T T T F F F T T F T F T T T T F F F T T F T F T T T T F F F T T F T F T F T F T T T T Relevant lines: 1, 5, 7, 8 Valid because on every line with all T premises, the conclusion is T.