Necessary or Sufficient

Question

Vitamin C prevents scurvy (a disease that kills due to a lack of vitamin C). Many fruits and vegetables contain vitamin C.

What type of condition is vitamin C to preventing scurvy?

I think that vitamin C is a necessary and sufficient condition because vitamin C is required to prevent scurvy and it is enough to prevent scurvy. Would I be right I think that it is necessary and sufficient?

Answer 1

The difference between necessary and sufficient conditions can be explained as follows:

1) Vitamin C is a sufficient condition for preventing scurvy

This means that scurvy can always be prevented by taking vitamin C. But there may be other ways as well.

2) Vitamin C is a necessary and sufficient condition for preventing scurvy

This means that scurvy can always be prevented by taking vitamin C, and it is the only possible way.

As far as I know, scurvy is a disease caused by a lack of vitamin C. Therefore, 2 seems to be the right answer.

Answer 2

Taking (or otherwise assimilating) vitamin C is sufficient to prevent scurvy if it can never be the case that X takes vitamin C and X gets scurvy (subject to a specified time period).

Taking (or otherwise assimilating) vitamin C is necessary to prevent scurvy if it can never be the case that X gets scurvy despite taking vitamin C (again subject to a specified time period).

In the terms in which your question is set, the answer seems then to be that taking vitamin C is both necessary and sufficient to prevent scurvy.

However, there is a sufficient condition within the sufficient condition : only if X takes a sufficient amount of vitamin C will scurvy be prevented. Also the necessity condition works only if a sufficient amount of vitamin C is applied in the prevention. An insufficient quantity of vitamin C is not necessary to the prevention of scurvy since it won't prevent scurvy at all.

Nice question.

Answer 3

To say something is neccesary is to say that x is imposible without y. Water is neccesary for human beings to maintain life. That is take away water from this person entirely and they will die. Removing all oxygen from a person will also cause death necessarily. There is no way out of the result which is what neccesary expresses.

If there is another option to cure scurvy then vitamin c is not neccesary. If there is no way to prevent scurvy without involving vitamin c in the cure, then you are correct that there is a neccesary relationship.

Sufficent expresses that the result is possible with x as in when you do x or x is present. But also you may be able to get the result without resorting to x. You can think of the sufficent is an at least one possible answer to the result.

Answer 4

The answer lies in your question:

a disease that kills due to a lack of vitamin C

1. If not the vitamin C, then the disease kills. (not A => B)
2. Therefore, if you are alive, then you have the required amount of the vitamin C. (not B => A, applying contrapositive here)

Here "being alive" is antecedent (a sufficient part), "having the required amount of the vitamin C" is consequent (a necessary part).

Also, you say

Vitamin C prevents scurvy

1. If there is sufficient amount of the vitamin C, then there is no scurvy.

Here, "there is sufficient amount of the vitamin C" is the antecedent (a sufficient part) and "no scurvy" is the consequent (a necessary part).

Hence, the vitamin C is both sufficient and necessary based on your definition.