Exercise Set 9.4

if the picture is a daguerreotype, then it has to have been made after 1837; and the man in the picture can't be Hegel if it was made after 1937. So it isn't Hegel in the picture if it's a daguerreotype.

Chain argument If A then not H If D then not H

If Casey goes to the meeting, then Simone will go. If Simone goes, then Chris will go. If Casey goes to the meeting, then Chris will go.

Chain argument If C then S. If S then X. If C then X.

If the stock is lightweight, then it's aluminum; but if it's aluminum, then it will be hard to weld. So, if the stock is lightweight, it will be hard to weld.

Chain argument If L then A If A then W If L then W

If the oil gusher in the gulf of Mexico continues until August, it will be ten times bigger than the Exxon Valdez spill. And if it's that much bigger than the Exxon Valdez, it'll be the biggest man-made environmental disaster ever.

Chain argument If O then V If V then D If O then D

Joel will automatically be accepted provided he got his forms in on time. Unfortunately he did not get his forms in on time; so he won't be automatically accepted.

Denying the Antecedent If F then A Not F Not A

If Jared studies really hard for the final, he will pass the course. (Later) Well, Jared didn't study for the final, so it's a sure thing he won't pass

Denying the Antecedent If S then P Not S Not P

This Zinfandel would have a smooth finish, if it came from very old vines. In fact, it does have a smooth finish, so it must have come from very old vines.

If O then Z Z O

If Shelley has read the Republic, then she's bound to know who Thrasymachus is. And since she clearly does know who Thrasymachus is, we can conclude that she must have read the Republic.

If R then T T R

The generator works. The generator works only if the polarity of the circuit has been reversed. The polarity of the circuit has been reversed.

Modus Ponens G If G then P P

Failure to melt at 2,600 degrees is sufficient for determining that this item is not made of steel. The item failed to melt at 2,600 degrees. The item is not made of steel

Modus Ponens If F then not S F Not S

If the referee scored the fight in favor of Madderly, the Madderly wins the decision. The referee did score the fight in favor of Madderly Therefore, Madderly wins the decision.

Modus Ponens If R then M R M

Madderly wins the decision provided the referee scored the fight in his favor. The referee did score the fight in favor of Madderly. Therefore, Madderly wins the decision

Modus Ponens If R then M R M

If the song is in A-minor, there are no black keys in its scale. However, there are black keys in its scale. The song is not in A-minor

Modus Tollens If A then B Not B Not A

If he got his forms in on time, he's automatically accepted. But he wasn't automatically accepted; consequently, he must not have gotten his forms in on time.

Modus Tollens If F then A Not A Not F

If the new generator will work, then the polarity of the circuit has been reversed. But the polarity of the circuit has not been reversed. The new generator will not work.

Modus Tollens If G then P Not P Not G

Bill was not with AT&T; but he'd have to have been with AT&T if he'd had an early iPhone. So he clearly did not have an early iPhone.

Modus Tollens Not A If P then A Not P

If you eat fish, you're a carnivore and if you're an omnivore, you must be a carnivore. So, if you eat fish, that would make you an omnivore.

Undistributed middle If F then C If O then C If F then O

If Robinson had some great success in business, he'd be well-known. Furthermore, if he were extremely rich, he'd be well-known. So, of course, if Robinson ad some great success in business, he'd be extremely rich.

Undistributed middle. If S then W If R then W If S then R