Necessary and sufficient Practice
Necessary Condition
Being 18 years of age is a necessary condition for being able to buy cigarettes legally in North Carolina. 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 Condition
Earning a total of 950 points (95%) in this Critical Thinking class is a sufficient condition for earning a final grade of A. If you have 950 points for the course, then it must follow that you will have a final grade of A.
Necessary Condition
Having gasoline in my car (I have a gasoline engine) is a necessary condition for my car to start. Without gasoline (x) my car (y) 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.
Necessary Condition
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.
Sufficient Condition
If we say that "x is a sufficient condition for y," then we mean that if we have x, we know that y must follow. In other words, x guarantees y.
(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.
Is attending class regularly and punctually a necessary or sufficient condition for being successful in class?
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.
Is being 20 years old a necessary or sufficient condition for being a college student?
Necessary Condition
Is being a female a necessary or sufficient condition for being a mother?
Being a male is a necessary condition for being a father since it is imposible 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.
Is being a male a necessary or sufficient condition for being a father?
Sufficient Condition
Is being a mother a necessary or sufficient condition for being a female?
Necessary Condition
Is being a rectangle a necessary or sufficient condition for being a square?
Sufficient Condition
Is being a square a necessary or sufficient condition for being a rectangle?
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.
Is completing all the requirements of your degree program a necessary or sufficient condition for earning your degree?
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.
Is having the flu virus in your blood a necessary or sufficient condition for being sick?
Not either, because a chimpanzee, for example, may have two arms, but it is not a human being. A war veteran may have lost both his arms, but he is a human being even so.
Is having two arms necessary or sufficient condition for being a human being?
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.
Is sunlight a necessary or sufficient condition for the roses to bloom?
Sufficient Condition
Pouring a gallon of freezing water on my sleeping daughter is sufficient to wake her up. If I pour the gallon of freezing water on her then its guaranteed that she will wake up.
Sufficient Condition
Rain pouring from the sky is a sufficient condition for the ground to be wet.
Necessary Condition
We've already said that "If A, then B," means that if we have A, then we know that B must follow. But then we also said that "A, only if B" means that if we do not have B, then we will not have A. These two conditional claims, "If A, then B" and "A, only if B" refer to two different kinds of conditions: necessary conditions and sufficient conditions.
