Put each of the following disjunctive syllogisms into standard form, identify the disjuncts and any implicit elements, and determine whether the syllogism is valid.

2.Either the circuit is broken or the light bulb is dead. But I know the bulb isn't dead, so the circuit must be broken.

11.Either human beings have free will or they are not responsible for their actions. But they are responsible, so they do have free will

17.Some economists believe that we can't have both low inflation and low unemployment. If that assumption is true, inflation must be low, because unemployment is high.

Identify the antecedent and consequent in each of the following statements, then put the statement into standard form (if it is not in standard form already).

3If a categorical syllogism has two negative premises, then it is not valid.

6.Prices rise if demand increases.

11.ll call you unless you call me first.

14.If we don't punish the use of cell phones with fines and tickets, then drivers won't pay attention to simple safety reminders.

For each of the following standard form syllogisms, identify its kind and determine whether the syllogism is valid.

5.If the lights are still working, then the battery is not dead. The lights are still working.

6.The battery is not dead.

If Rome had enlisted the efforts of all citizens, it could have repelled invaders. Rome did not enlist the efforts of all its citizens.

Integrative Exercise Put each of the following hypothetical syllogisms into standard form, identify any implicit premise or conclusion, identify what type of hypothetical syllogism it is, and determine whether the syllogism is valid.

3.f I take the new job, I'll have a longer commute, and if I have a longer commute, I will need a new car. So I'll need a new car if I take the new job.

5.If you leave the milk out of the refrigerator, it will sour. The milk soured, so you must have left it out.

15If God had wanted people to fly, He would not have given us Buicks. But He has given us Buicks; therefore . . .