More on Necessary and Sufficient Conditions

A is necessary for B iff (“if and only if”) B cannot occur without A. Whenever you have B, you have A.

A is sufficient for B iff A guarantees B.

Whenever you have A, you have B.

Examples:

Necessary Conditions
If we say that "A is a necessary condition for B," we mean that if we don't have A, then we won't have B. Or put differently, without A, you won't have B. To say that Ax is a necessary condition for B does not mean that A guarantees B.

Examples:
Having gasoline in my car (I have a gasoline engine) is a necessary condition for my car to start. Without gasoline (A) my car (B) will not start. Of course, having gasoline in the car does not guarantee that my car will start. There are many other conditions needed for my car to start.

Having oxygen in the earth's atmosphere is a necessary condition for human life. Certainly, having oxygen will not guarantee human life. There are many other conditions needed for human life other than oxygen in the atmosphere.

Being 18 years of age is a necessary condition for being able to buy cigarettes legally in Nanaimo. Of course, being 18 does not guarantee that a person will buy cigarettes. There are many other conditions that lead to a person buying cigarettes than being 18 years of age.

Sufficient Conditions
If we say that "A is a sufficient condition for B," then we mean that if we have A, we know that B must follow. In other words, A guarantees B.

Examples:
Getting a total of 95% in this class is a sufficient condition for earning a final grade of A. If you have 95% for the course, then it must follow that you will have a final grade of A.

Pouring a gallon of freezing water on my sleeping dog is sufficient to wake her up. If I pour the gallon of freezing water on her then its guaranteed that she will wake up.

Rain pouring from the sky is a sufficient condition for the ground to be wet.

Please note that in none of these example is the sufficient condition also a necessary condition.

For example, it is not necessary to get 95 % to earn an A in this course. You can earn 92 % to earn an A. (We cannot say that if you do not get 95 % then you can't have an A.)

It is not necessary to pour a gallon of freezing water on my dog to wake her up. (A wrecking ball against the wall will do it as well.)

Similiarly, it is not necessary for rain to be pouring from the sky for the ground to be wet. The sprinkler could be on as well.

Test your knowledge of necessary and sufficient conditions by trying the following:

1.     Is sunlight a necessary or sufficient condition for the roses to bloom?

2.     Is earning a final grade of C a necessary or sufficient condition for passing the course?

3.     Is being a male a necessary or sufficient condition for being a father?

4.     Is earning 120 credits a necessary or sufficient condition for earning a degree at MUC?

5.     Is having the flu virus in your blood a necessary or sufficient condition for being sick?

6.     Is attending class regularly and punctually a necessary or sufficient condition for being successful in class?

7.     Is being 20 years old a necessary or sufficient condition for being a college student?

8.     Is completing all the requirements of your degree program a necessary or sufficient condition for earning your degree?

Answers

1. Is sunlight a necessary or sufficient condition for the roses to bloom?

Sunlight is a necessary condition for the roses to bloom, since without sunlight it would be impossible for the roses to bloom.  It is not a sufficient condition, though, because sunlight alone does not guarantee that the roses will bloom.

2. Is earning a final grade of C a necessary or sufficient condition for passing the course?

Earning a final grade of C is a sufficient condition for passing this course because earning a C guarantees passing it.  It is not a necessary condition because there are other ways to pass the course other than earning final grade of C.

3. Is being a male a necessary or sufficient condition for being a father?

Being a male is  a necessary condition for being a father since it is impossible to be a father without being a male.  Being a male is not a sufficient condition, however, since being a male does not guarantee that a male will be a father.

4. Is earning 120 credits a necessary or sufficient condition for earning a degree at MUC?

Earning 120 credits is a necessary condition for earning a degree since without 120 earned hours it is impossible to earn a degree.  Earning 12 credits is not sufficient, however, because earning 120 credits does not guarantee that one will earn a degree.

5. Is having the flu virus in your blood a necessary or sufficient condition for being sick?

Having a flu virus is sufficient for being sick, but not necessary since there are other ways to be sick besides having a flu virus.

6. Is attending class regularly and punctually a necessary or sufficient condition for being successful in class?  

(with the exception of a very small number of students) For most people attending class regularly and punctually is a necessary condition for being successful in class.

7. Is being 20 years old a necessary or sufficient condition for being a college student?

Being 20 years old is neither necessary nor sufficient for being a college student.  One can be a college students without being 20 years old, and there are other ways to be a college student than being 20 years old.

8. Is completing all the requirements of your degree program a necessary or sufficient condition for earning your degree?

Completing all of your requirements is both a necessary and sufficient condition for earning your degree.  Without completing all requirements, it is impossible to earn a degree, and completing all requirements guarantees earning a degree.