Necessary and Suffcient Causes

These two types of causes go hand in hand, so I wanted to detail both. To lay them out, I will be using P and Q as my variables.

Necessary causes are when the statement implies that the consequent Q, is true. If P is a cause of Q, then the presence of Q implies that there is P. However, the presence of P does not necessarily mean the presence of Q. Basically, if something is necessary to cause the other, then the second thing can't happen without the first.

Sufficient causes are when P is a sufficient cause of Q, and the presence of P implies the presence of Q. Another variable X can also cause Q, and Q does not imply the presence of P. It also means that every time something happens, the outcome will follow.

You can have four combinations of this.
Both.
Necessary and not sufficient,
Sufficient and not necessary
or neither.

Confusing I know, but here are some examples.

Necessary and not sufficient - HIV is a necessary cause of AIDS, but not everyone who gets HIV will get AIDS.
Sufficient and not necessary - Exploding spontaneously is a sufficient cause of death, but there are a lot of other causes of death.
Both - A mutation associated with a disease. 100% of people who have this mutation will have this disease. Those without the mutation, will never have the disease.
Neither - Smoking is not a sufficient or necessary cause of lung cancer because you can get lung cancer and never smoke, and smoke and never get lung cancer.