Looking to get some help with some philosophy questions Im taking in my spare time

Looking to get some help with some philosophy questions Im taking in my spare time. 

Necessary and Sufficient Conditions

“People who smoke are much more likely to develop lung cancer than are people who don’t; of course, some people who do not smoke also develop lung cancer, and many smokers never develop lung cancer.”

That statement claims that smoking is what sort of condition for lung cancer?

a. necessary

b. sufficient

c. necessary and sufficient

d. neither necessary nor sufficient

“If we are going to have a real democracy, then we must place limits on how much money the wealthy can spend to control elections.”

Limits on money spent to control elections is ______ condition for a real democracy.

a. a necessary

b. a sufficient

c. a necessary and sufficient

d. neither a necessary nor a sufficient

“Muddy Mother will not win unless the track is muddy.”

A muddy track is ______ condition for Muddy Mother’s winning the race.

a. a necessary

b. a sufficient

c. a necessary and sufficient

d. neither a necessary nor a sufficient

“A heavy rain within the next 3 days is our only hope for saving the wheat crop.”

A heavy rain within the next 3 days is ______ condition for saving the wheat crop.

a. a necessary

b. a sufficient

c. a necessary and sufficient

d. neither a necessary nor a sufficient

“I would go on a date with Bruce only if he owned a bright red Porsche.” That statement means that:

a. Bruce owning a bright red Porsche is a necessary condition for my going on a date with

Bruce.

b. Bruce owning a bright red Porsche is a sufficient condition for my going on a date with Bruce.

c. Bruce owning a bright red Porsche is both a necessary and a sufficient condition for my going on a date with Bruce.

d. Bruce owning a bright red Porsche is neither a necessary nor a sufficient condition for my going on a date with Bruce.On conditional arguments: For each argument, symbolize the conditional argument, and then determine whether it as valid or invalid. If it is valid, which argument form does it instantiate? (modus ponens or modus tollens)

1. If the defendant had carried a pistol, then she would be guilty. But she is obviously not guilty, since she did not carry a pistol

2. If this exam is too hard, then critical thinking students will look tired and miserable. So obviously this exam is indeed too hard, since critical thinking students look extremely tired and

Miserable.

3. If the murder weapon did not belong to Jones, then we might conclude that Jones is not guilty. But in fact it has been conclusively proved that the murder weapon did belong to Jones. So we must conclude that Jones really is guilty

4. Robert is guilty of negligent homicide only if he did not exercise due caution. But Robert is a careful driver, and he was exercising due caution. So we must find Robert not guilty of negligent

Homicide.

5. Bruce is guilty of check fraud only if he knew there was no money in his account. But Bruce certainly did not know that there was no money in his account: He is a complete idiot about everything related to finances. So Bruce is not guilty of check fraud.